Department of Mathematical Sciences

Applicable and Computational Algebra Publications

Books
  • Alfred J. Menezes (Editor), Ian F. Blake, XuHong Gao, Ronald C. Mullin, Scott A. Vanstone and Tomic Yaghoobian, Applications of Finite Fields, Kluwer Academic Publishers, Boston/Dordrecht/Lancaster, 1993.
  • E. F. Assmus, Jr. and J. D. Key, Designs and their Codes, Cambridge Tracts in Mathematics No. 103, Cambridge University Press, 1992. (paperback edition, 1994).
  • J. V. Brawley and G. E. Schnibben, Infinite Algebraic Extensions of Finite Fields, Contemporary Mathematics, Vol. 95, A.M.S., Providence R.I., 1989  (reprinted, 1992).
  • J. V. Brawley and S. M. Lukaecki, Problem Solving for High School Teachers with the Sharp EL 5200 Calculator, Clemson University Department of Mathematical Sciences, Clemson, SC 1991.
Chapters in Books
  1. Joel V. Brawley and Shuhong Gao, Mathematical Models in Classical Cryptology,  in Applied Mathematical Modeling: A Multidisciplinary Approach (D. R. Shier and K. T. Wallenius, Eds.), Chapman & Hall/CRC, Boca Raton, 2000,  93--113.
  2. Joel V. Brawley and Shuhong Gao, Mathematical Models in Public-key Cryptology, in Applied Mathematical Modeling : A Multidisciplinary Approach (D. R. Shier and K. T. Wallenius, Eds.),  Chapman & Hall/CRC, Boca Raton, 2000, 115--136.
  3. Joel V. Brawley, Vector Spaces in  Handbook of Discrete and Combinatorial Mathematics, CRC Press, 2000,  361-369.
  4. Joel V. Brawley, Linear Transformations, in Handbook of Discrete and Combinatorial Mathematics, CRC Press, 2000, 371-376.
  5. J. D. Key, Some error-correcting codes and their  applications, in  Applied Mathematical Modeling: A Multidisciplinary Approach (D. R. Shier and K. T. Wallenius, Eds.),  Chapman & Hall/CRC, Boca Raton, FL, 2000, 291--314.
  6. J. D. Key and E.F. Assmus, Jr., Polynomial Codes and Finite Geometries in "Handbook of Coding Theory", Vol. 2  (V.S. Pless and   W.C. Hufffman, Eds.), Elsevier, 1998, 1269--1343.
Recent papers: preprint, submitted, or to appear
  1. J. D. Key, J. Moori and B. G. Rodrigues, Ternary codes from graphs on triples. Discrete Math. (To appear)
  2. W. Fish, J.D. Key and E. Mwambene, Codes, designs and groups from the Hamming graphs, J. Combin. Inform. System Sci.(To appear)
  3. J. D. Key and J. Moori, Some irreducible codes invariant under the Janko group, J1 or J2. (Submitted)
  4. J. D. Key, T. P. McDonough and V. C. Mavron, Reed-Muller codes and permutation de- coding, Discrete Math. (To appear)
  5. W. Fish and J. D. Key and E. Mwambene, Binary codes from designs from the reflexive n-cube, Util. Math. (To appear)
  6. W. Fish and J. D. Key and E. Mwambene, Binary codes of line graphs from the n-cube, J. Symbolic Comput. (To appear)
  7. J. D. Key and J. Moori and B. G. Rodrigues, Codes associated with triangular graphs, and permutation decoding. (Submitted)
  8. J. D. Key and B. G. Rodrigues. Codes from lattice graphs, and permutation decoding. (Submitted)
  9. Dimitrova, E.S. (2008), Design of Experiment for Finite Dynamical Systems Models. Submitted.
  10. Dimitrova, E. S. Estimating the relative volumes of the cones in a Groebner fan. Submitted.
  11. Dimitrova, E.S., Jarrah, A.S., Laubenbacher, R., Probabilistic Dynamical Systems for Reverse Engineering of the Yeast Cell Cycle Network. Submitted.
  12. V.S.A. Kumar, M. Macauley, and H.S. Mortveit, Limit Set Reachability in Asynchronous Graph Dynamical Systems, To appear in LNCS proceedings of Reachability Problems, 2009. Palaiseau, France.
  13. M. Macauley, and H.S. Mortveit, Update Sequence Stability in Graph Dynamical Systems, Submitted to Discrete Contin. Dyn. Syst. Ser. S, 2009.
  14. M. Macauley, J. McCammond, and H.S. Mortveit, Dynamics Groups of Asynchronous Cellular Automata. Submitted, 2009. arXiv
  15. M. Macauley and H.S. Mortveit, Combinatorial Characterizations of Admissible Coxeter Sequences and Their Applications. Submitted to Discrete Math., 2009.
  16. G. L. Matthews, On Weierstrass semigroups of some triples on norm-trace curves, Lecture Notes in Computer Science, to appear. PDF file
  17. N. Drake and G. L. Matthews, Parameter choices and a better bound on the list size in the Guruswami-Sudan algorithm for algebraic geometry codes, in review. PDF file
  18. G. L. Matthews, Viewing multipoint codes as subcodes of one-point codes, Grobner Bases, Coding, and Cryptography, RISC Book Series (Springer), to appear. PDF file
    19. 2009
  19. Shuhong Gao, Daqing Wan and Mingsheng Wang,  Primary decomposition of zero-dimensional ideals over finite fields, Mathematics of Computation, 78 (2009), 509--521. PDF file (154K)
  20. Shuhong Gao and D. Frank Hsu, Short containers in Cayley graphs, Discrete Applied Mathematics, 157 (2009), 1354--1363. PS file (336K) or PDF file (135K)
  21. Jessie F. Burkhart, Neil J. Calkin, Justine C. Hyde-Volpe, Shuhong Gao, Kevin James, Hiren Maharaj, Shelly Manber, Jared Ruiz and Ethan Smith, Finite field towers and elements of high order arising from modular curves, Designs, Codes and Cryptography, 51 (2009), 301--314.
  22. J. D. Key, J. Moori and B. G. Rodrigues, Partial permutation decoding of some binary codes from graphs on triples, Ars Combin. 91 (2009), 363-371
  23. W. Fish, J.D. Key and E. Mwambene, Graphs, designs and codes related to the n-cube, Discrete Math., 309 (2009), 3255-3269. PDF file
  24. J. D. Key ,T. P. McDonough and V. C. Mavron, An upper bound for the minimum weight of the dual codes of desarguesian planes, European J. Combin., 30 (2009), 220-229. PDF file
  25. Laubenbacher, R., Jarrah, A.S., Dimitrova, Stiglere, B., Vera-Licona, P, System identification for discrete polynomial models of gene regulatory networks, Accepted by 15th IFAC Symposium on System Identification (SYSID 2009).
  26. Dimitrova, E.S., Garcia-Puente, L.D., Hinkelmann, F., Jarrah, A.S., Laubenbacher, R., Brandilyn Stigler, Vera-Licona, P., Parameter estimation for Boolean models of biological networks. Journal of Theoretical Computer Science, 2009. Invited paper.
  27. M. Macauley and H.S. Mortveit, Cycle Equivalence of Graph Dynamical Systems, Nonlinearity 22 (2009) 421-436. PDF file | arXiv
  28. G. L. Matthews, Frobenius numbers of generalized Fibonacci semigroups, Combinatorial Number Theory, 117-124, de Gruyter, Berlin, 2009. PDF file
  29. R. C. Laskar, G. L. Matthews, B. Novick and J. Villalpando, On irreducible no-hole L(2,1) coloring of trees, Networks 53 (2009), no. 2, 206-211. PDF file
    30. 2008
  30. Guantao Chen, Shuhong Gao and Zhiquan Hu,  Linked Graphs with Restricted Lengths, J. Combinatorial Theory, series B, 98 (2008), 735--751. PDF file (282K)
  31. J. D. Key and P. Seneviratne, Permutation decoding of codes from lattice graphs, Discrete Math., 308 (2008), 2862-2867
  32. J. D. Key, T. P. McDonough and V. C. Mavron, Partial permutation decoding for codes from finite affine geometry designs, J. Geom. 88 (2008), 101-109
  33. J. D. Key and J. Moori. Correction to: Designs, codes and graphs from the Janko groups J1 and J2, [J. Combin. Math. & Combin. Comput., 40 (2002), 143 - 159] J. Combin. Math. & Combin. Comput., 64 (2008), 153.
  34. D. Ghinelli, M.J. de Resmini and J.D. Key, Minimum words of codes from affine planes, J. Geom., 91 (2008), 43-51. PDF file
  35. Dimitrova, E.S., Zardecki, A. Forecasting Polynomial Dynamics (2008), Applied Mathematics and Computation, 204(1), pp. 233-239.
  36. Dimitrova, E.S., McGee, J., Laubenbacher, R., Vera Licona, P., Comparison of Discretization Methods for Network Inference, to apprear in Journal of Computational Biology.
  37. M. Macauley and H.S. Mortveit. On Enumeration of Conjugacy Classes of Coxeter Elements. Proc. Amer. Math. Soc. 136 (2008), 4157-4165. PDF file | arXiv
  38. M. Macauley, J. McCammond, and H.S. Mortveit. Order Independence in Asynchronous Cellular Automata. J. Cell. Autom. 3 (2008) 37-56. arXiv
  39. J. L. Kim and G. L. Matthews, Quantum error-correcting codes from algebraic curves, in Advances in Algebraic Geometry Codes, Series on Coding Theory and Cryptology (World Scientific, 2008), vol. 5; E. Martinez-Moro, C. Munuera, and D. Ruano, eds.; 419-444. PDF file
  40. R. E. Jamison and G. L. Matthews, On the acyclic chromatic number of Hamming graphs, Graphs and Combinatorics 24 (2008), 349-360. PDF file
  41. R. E. Jamison and G. L. Matthews, Acyclic colorings of products of cycles, Bulletin of the Institute of Combinatorics and its Applications 54 (2008), 59-76. PS file  PDF file
    42. 2007
  42. Shuhong Gao and Beth Novick,  Fault Tolerance of Cayley Graphs, Annals of Combinatorics, 11 (2007), 161--171. PDF file (186K)
  43. J. D. Key and P. Seneviratne, Permutation decoding for binary self-dual codes from the graph Qn where n is even, Advances in Coding Theory and Cryptology, Series on Coding Theory and Cryptology, 2. World Scientic Publishing Co. Pte. Ltd., Hackensack, NJ, 2007. Editors: T. Shaska, W. C. Hu man, D. Joyner, V. Ustimenko, pp. 152-159
  44. J. D. Key and P. Seneviratne, Binary codes from rectangular lattice graphs and permutation decoding, European J. Combin. 28 (2007), 121-126 PDF file
  45. J. D. Key and P. Seneviratne, Permutation decoding for binary codes from the line graphs of complete multipartite graphs, Discrete Math. 307 (2007), 2217-2225
  46. J. D. Key and F. F. Ngwane, A lower bound for the minimum weight of the dual 7-ary code of a projective plane of order 49 Des, Codes Cryptogr. 44 (2007), 133-142
  47. E. S. Dimitrova, A. S. Jarrah, R. Laubenbacher, and B. Stigler (2007), A Groebner fan method for biochemical network modeling, In Proc. International Symposium on Symbolic and Algebraic Computation (ISSAC), ACM, pp. 122-126.
  48. G. L. Matthews and R. S. Robinson, A variant of the Frobenius problem and generalized Suzuki semigroups, Combinatorial Number Theory, 363-369, de Gruyter, Berlin, 2007. PS file PDF file
    49. 2006
  49. Jeff Farr and Shuhong Gao, Gröbner bases and generalized Padé approximation, Mathematics of Computation, 75 (2006), 461-473. PSfile (424K) or PDF file (154K)
  50. Jeff Farr and Shuhong Gao, Computing Grobner bases for vanishing ideals of finite sets of points, Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC16), LNCS 3857, 2006, 118--127. PSfile (390K) or PDF file (144K)
  51. J. D. Key, J. Moori and B. G. Rodrigues, Permutation decoding of codes from graphs on triples, Ars Combin. 79 (2006), 11-19 PDF file
  52. J. D. Key, T. P. McDonough and V. C. Mavron, Information sets and partial permutation decoding for codes from finite geometries, Finite Fields Appl. 12 (2006), 232-247 PDF file
  53. J. D. Key, Recent developments in permutation decoding, Notices of the South African Mathematical Society, 37/1 (2006), 2-13 PDF file
  54. R. E. Jamison, G. L. Matthews, and J. Villalpando, Acyclic colorings of products of trees, Information Processing Letters 99 (2006), no. 1, 7-12. PS file PDF file
  55. H. Maharaj and G. L. Matthews, On the floor and the ceiling of a divisor, Finite Fields and their Applications 12 (2006), no. 1, 38-55. PS file  PDF file
  56. M. A. Coleman, N. Drake, and G. L. Matthews, Codes from a quotient of the Hermitian curve attaining the designed distance, Congressus Numerantium 182 (2006), 161-170.
  57. R. E. Jamison and G. L. Matthews, Distance k colorings of Hamming graphs, Congressus Numerantium 183 (2006), 193-202. PS file PDF file
    58. 2005
  58. Jeffrey B. Farr and Shuhong Gao,  Gröbner bases, Padé  approximation, and decoding of linear codes, Coding Theory and Quantum Computing, Contemporary Mathematics, vol.381, Amer. Math. Soc., Providence, RI, 3--18, 2005.    PSfile (404K) or PDF file (147K)
  59. J. D. Key, T. P. McDonough and V. C. Mavron, Partial permutation decoding of codes from finite planes, European J. Combin., 26/5 (2005), 665-682 PDF file
  60. J. D. Key and J. Limbupasiriporn, Partial permutation decoding of codes from Paley graphs, Congr. Numer. 170 (2005), 143-155 PDF file
  61. J. D. Key, J. Moori and B. G. Rodrigues, Some binary codes with automorphism group containing the symplectic group of odd characteristic, Util. Math. 67 (2005), 121-128
  62. G. L. Matthews, Weierstrass semigroups and codes from a quotient of the Hermitian curve, Designs, Codes and Cryptography 37 (2005), no. 3, 473-492.  PS file  PDF file
  63. G. L. Matthews and T. W. Michel, One-point codes using places of higher degree, IEEE Transactions on Information Theory 51 (2005), no. 4, 1590-1593. PS file  PDF file
  64. G. L. Matthews, On integers nonrepresentable by a generalized arithmetic progression, Topics in Combinatorial Number Theory, DIMITIA ITI 261, 2005, 143-148. PS file PDF file
  65. G. L. Matthews, Some computational tools for estimating the parameters of an algebraic geometry code, Coding Theory and Quantum Computing, 119-126, Contemporary Mathematics 381, Amer. Math. Soc., Providence, RI, 2005. PS file PDF file
  66. H. Maharaj, G. L. Matthews, and G. Pirsic, Riemann-Roch spaces for the Hermitian curve with applications to algebraic geometry codes and low-discrepancy sequences, Journal of Pure and Applied Algebra 195 (2005), 261-280.PS file or PDF file
    67. 2004
  67. Shuhong Gao, Erich Kaltofen, John P. May, Zhengfeng Yang and Lihong Zhi,  Approximate factorization of multivariate polynomials via differential equations, in Proceedings of the 2004 international symposium on Symbolic and algebraic computation (ISSAC 2004, July 4-7, 2004,  University of Cantabria, Santander, Spain), pp. 167-174.  PSfile (232K) or PDF file (171K) Maple software available at Erich Kaltofen or Lihong Zhi 
  68. Joel V. Brawley and Shuhong Gao, On density of primitive elements for field extensions, preprint, 2004 (6 pages).  PSfile (280K) or PDF file (94K)
  69. Shuhong Gao and Alan G.B. Lauder, Fast absolute irreducibility testing via Newton polytopes, preprint 2004 (14 pages). PSfile (273K) or PDF file (95K)
  70. Fatima Abu Salem, Shuhong Gao and Alan G.B. Lauder, Factoring polynomials via polytopes, in Proceedings of the 2004 international symposium on Symbolic and algebraic computation (ISSAC 2004, July 4-7, 2004,  University of Cantabria, Santander, Spain), pp.  4-11.  PSfile (419K) or PDF file (231K)
  71. J. D. Key, J. Moori and B. G. Rodrigues, Permutation decoding for the binary codes from triangular graphs, European J. Combin., 25, (2004), 113-123 PDF file
  72. J. D. Key, J. Moori and B. G. Rodrigues, Binary codes from graphs on triples, Discrete Math., 282/1-3 (2004), 171-182 PDF file
  73. G. L. Matthews, Codes from the Suzuki function field, IEEE Transactions on Information Theory 50 (2004), no. 12, 3298-3302. PS file PDF file
  74. G. L. Matthews, On numerical semigroups generated by generalized arithmetic sequences, Communications in Algebra 32 (2004), no. 9, 3459-3469.PS file  PDF file
  75. G. L. Matthews, The Weierstrass semigroup of an m-tuple of collinear points on a Hermitian curve, Lecture Notes in Computer Science 2948 (2004), 12-24. PS file PDF file
    76. 2003
  76. Shuhong Gao, Virginia M. Rodrigues and Jeffrey Stroomer, Grobner basis structure of finite sets of points, preprint, 2003 (16 pages). PSfile (441K) or PDF file (166K)
  77. Shuhong Gao, A new algorithm for decoding Reed-Solomon codes, in Communications, Information and Network Security (V. Bhargava, H. V. Poor, V. Tarokh and S. Yoon, Eds.), Kluwer Academic Publishers, 2003, pp. 55-68. PS file (340K) or PDF file (118K)
  78. Shuhong Gao, Factoring multivariate polynomials via partial differential equations, Mathematics of Computation 72 (2003), 801--822. PS file (502K) or PDF file (201K)
  79. Shuhong Gao and Virginia M. Rodrigues, Irreducibility of polynomials modulo p via Newton Polytopes,  Journal of Number Theory 101 (2003), 32-47. PS file (411K) or PDF file (142K)
  80. Richard P. Brent, Shuhong Gao and Alan G.B. Lauder, Random Krylov spaces over finite fields, SIAM J. on Discrete Mathematics 16 (2003), 276-287. PS file (340K) or PDF file (131K)
  81. J. D. Key and M. J. de Resmini, An upper bound for the minimum weight of dual codes of Figueroa planes, J. Geometry, 77 (2003), 102-107
  82. J. D. Key, J. Moori and B. G. Rodrigues, On some designs and codes from primitive repre- sentations of some finite simple groups, J. Combin. Math. & Combin. Comput. 45 (2003), 3-19
  83. K. L. Clark, L. Hat eld, J.D. Key and H.N.Ward, Dual codes of planes of order 25, Advances in Geometry, 3 (2003) Special Issue, 140-152 PDF file
  84. D. E. Dobbs and G. L. Matthews, On a question of Wilf concerning numerical semigroups, International Journal of Commutative Rings 2 (2003), no. 4, 195- 204. PS file PDF file
    85. 2002
  85. Shuhong Gao and Virginia M. Rodrigues, Irreducibility of polynomials modulo p via Newton Polytopes,  Journal of Number Theory. (to appear, 13 pages) PS file (411K) or PDF file (142K)
  86. Shuhong Gao and Alan G.B. Lauder, Hensel lifting and polynomial factorisation, Mathematics of Computation, 71 (2002), 1663-1676). [More]
  87. Huapeng Wu, M. Anwar Hasan, Ian F. Blake and Shuhong Gao, Finite fields multiplier using redundant representation, IEEE Transactions on Computers, vol. 51, no. 11, 2002, 1306--1316. PDF file (150K)
  88. J. D. Key and J. Moori. Designs, codes and graphs from the Janko groups J1 and J2, J. Combin. Math. & Combin. Comput., 40 (2002), 143 - 159 PDF file
  89. Peng Ding and Jennifer D. Key, Subcodes of projective generalized Reed-Muller codes spanned by minimum-weight vectors Des, Codes Cryptogr., 26 (2002), 197-211 PDF file
  90. K. L. Clark, J. D. Key and M. J. de Resmini, Dual codes of translation planes, European J. Combin., 23 (2002), 529-538 PDF file
  91. G. L. Matthews, On triply-generated telescopic semigroups and chains of semigroups, Congressus Numerantium 154 (2002), 117-123. PS file  PDF file
    92. 2001
  92. Richard P. Brent,  Shuhong Gao and Alan G.B. Lauder, Random Krylov spaces over finite fields,  SIAM J. Discrete Mathematics. (to appear, 17 pages) PS file (340K) or PDF file (131K)
  93. Shuhong Gao, Erich Kaltofen and Alan G.B. Lauder, Deterministic distinct degree factorization for polynomials over finite fields, preprint 2001.  (10 pages) PDF file (210K)
  94. Joel V. Brawley, Shuhong Gao and Donald Mills, Associative Rational functions in two variables,  in  Finite Fields and Their Applications   (D. Jungnickel and H. Niederreiter, Eds.), Springer-Verlag, 2001, 43--56. PS file (336K) or PDF file (120K)
  95. Shuhong Gao, Abelian groups, Gauss periods, and normal bases, Finite Fields and Their Applications 7 (2001), 149--164. PS file (410K) or PDF file (151K)
  96. Shuhong Gao, Absolute irreducibility of polynomials via Newton polytopes, J. of Algebra 237 (2001), 501--520. gzipped PS file (502K) or PDF file (200K)
  97. Shuhong Gao, On the deterministic complexity of polynomial factoring, J. Symbolic Computation 31 (2001), 19--36. [More] 
  98. Shuhong Gao and Alan G.B. Lauder, Decomposition of polytopes and polynomials, Discrete and Computational Geometry   26 (2001), 89--104. PS file (365K) or PDF file (133K)
  99.  J. D. Key,  Some applications of Magma in designs and codes: oval designs,  hermitian unitals and generalized Reed-Muller codes, J. Symbolic Comput. 31 (2001), 37--53. PDF file
  100.  J. D. Key and M. J. de Resmini, Ternary dual codes of the planes of order nine, J. Statist. Plann.  Inference 95 (2001), 229 -- 236. PDF file
  101. Dimitrova E.S., Yordanov, O. (2001). Statistics of Some Low-dimensional Chaotic Flows. International Journal of Bifurcation and Chaos, 11(10), pp. 2675-2682.
  102. D. E. Dobbs and G. L. Matthews, On comparing two chains of numerical semigroups and detecting Arf semigroups, Semigroup Forum 63 (2001), no. 2, 237-246. PS file PDF file
  103. G. L. Matthews, Weierstrass pairs and minimum distance of Goppa codes, Designs, Codes and Cryptography 22 (2001), no. 2, 107-121. PS file  PDF file
    104. 2000
  104. Shuhong Gao, Joachim von zur Gathen, Daniel Panario and Victor Shoup, Algorithms for exponentiation in finite fields, J. Symbolic Computation 29 (2000), 879-889. PDF file (306K)
  105. Shuhong Gao and M. Amin Shokrollahi, Computing roots of polynomials over function fields of curves, in Coding Theory and Cryptography: From Enigma and Geheimschreiber to Quantum Theory (D. Joyner, Ed.), Springer, 2000, 214--228. gzipped PS file (79K) or PDF file (212K)
  106.  J. D. Key and K. Mackenzie-Fleming, Rigidity theorems for a class of affine resolvable designs, J. Combin. Math. & Combin. Comput. 35 (2000), 147--160. PDF file
  107.  Peng Ding and Jennifer D. Key, Minimum-weight codewords as generators of generalized Reed-Muller codes, IEEE Trans. Inform. Theory 46 (2000), 2152 -- 2158. PDF file
  108.  Joel V. Brawley, In Memoriam:  Leonard Carlitz (1907-1999),  Finite Fields and Their Applications 6: 203-206 (2000).
    1999
  109. Shuhong Gao, Elements of provable high orders in finite fields, Proc. American Math. Soc. 127  (1999), 1615--1623. PDF file (153K)
  110. Shuhong Gao and Jason Howell, A general polynomial sieve, Designs, Codes and Cryptography 18 (1999), 149--157.  gzipped PS file (504K) or PDF file (118K)
  111. Shuhong Gao, Jason Howell and Daniel Panario, Irreducible polynomials of given forms, Contemporary Mathematics, vol. 225, Amer. Math. Soc., Providence, RI, 1999, 43--54. PS file (404K) or PDF file (146K)
  112. Joel V. Brawley, Shuhong Gao and Donald Mills, Computing composed products of polynomials, Contemporary Mathematics, vol. 225, Amer. Math. Soc., Providence, RI, 1999, 1--15. 
  113.  Neil J. Calkin, Jennifer D. Key, and Marialuisa J. de Resmini, Minimum weight and dimension formulas for some geometric codes, Des. Codes Cryptogr. 17 (1999), 105--120.  PDF file
  114. J.  D. Key and F. E. Sullivan, Steiner systems from binary codes, Ars Combin. 52 (1999), 153--159.
  115. K. L. Clark and J. D. Key, Geometric codes over fields of odd prime power order, Congr. Numer. 137 (1999), 177 - 186. PDF file
  116. J. V. Brawley and T. Mateer, Video Poker in South Carolina: A Mathematical Study, The SC Digest, Strom Thurmond Institute, Clemson University, 1999.
    117. 1998
  117. Shuhong Gao, Beth Novick and Ke Qiu, From Hall's matching theorem to optimal routing on hypercubes, J. Combinatorial Theory (B) 74 (1998), 291--301. PDF file (138K)
  118. S. Gao and J. D. Key, Bases of minimum-weight vectors for codes from designs, Finite Fields and Their Applications  4 (1998), 1--15. PDF file (187k)
  119. Shuhong Gao, Joachim von zur Gathen and Daniel Panario, Gauss periods: orders and cryptographical applications, Mathematics of Computation,  67 (1998), 343--352. gzipped PS file (46k)
  120. J. D. Key, Codes and finite geometries, Congr. Numer. 131 (1998), 85--99. 
  121. J. D. Key and M. J. de Resmini,  Small sets of even type and codewords, J. Geom. 61 (1998), 83--104. PDF file
  122. J. V. Brawley and T. Teitloff, Similarity to Symmetric Matrices over Finite Fields, Finite Fields and Applications 4 (1998),  261-274.
    1997
  123. Shuhong Gao and Daniel Panario, Density of normal elements, Finite Fields and Their Applications  3 (1997), 141--150. PS file (169k)
  124. Shuhong Gao and Daniel Panario, Tests and constructions of irreducible polynomials over finite fields, Foundations of Computational Mathematics  (F. Cucker and M. Shub, Eds.), Springer, 346--361, 1997. PDF file (249k)
  125. Ian  F.  Blake, Shuhong Gao and Ronald C.  Mullin, Specific irreducible polynomials with linearly independent roots over finite fields, Linear Algebra and Its Applications 253 (1997), 227--249. PDF file (157k)
  126.  J. D. Key and V. D. Tonchev, Computational results for the known biplanes of order 9, 113-122, in Geometry, Combinatorial Designs, and Related Structures (Editors: J.W.P. Hirschfeld and S. Magliveras and M.J. de Resmini), Cambridge University Press, Cambridge, London Math. Soc. Lecture Note Series 245  (1997). PDF file
  127.  J. D. Key, B. Novick, and F. E. Sullivan, Binary codes of structures dual to unitals, Congr. Numer. 123 (1997), 119--124.
  128.  J. D. Key and F. D. Shobe, Some transitive Steiner triple systems of Bagchi and Bagchi, J. Statist. Plann.  Inference, 58 (1997) 79-86.
    1996
  129. Ian  F. Blake, Shuhong Gao and Robert L. Lambert, Construction and distribution problems for irreducible trinomials over finite fields, in  Applications of Finite Fields (D. Gollmann, Ed.),  Oxford, Clarendon Press,  1996, 19--32. PS file (195k)
  130. E. F. Assmus, Jr. and J. D. Key, Designs and codes: an update, Des. Codes Cryptogr., 9 (1996), 7-27. PDF file
  131. L. L. Carpenter and J. D. Key, Oval designs and Reed-Muller codes, J. Combin. Math. & Combin. Comput.,22 (1996), 79-85.
  132. J. D. Key, Extendable Steiner designs from finite geometries, J. Statist. Plann.  Inference, 56 (1996), 181-186.
    1995
  133. Shuhong Gao and Scott A. Vanstone, On orders of optimal normal basis generators, Mathematics of Computation  64 (1995), 1227--1233.  PDF file (92k)
  134. Shuhong Gao, Joachim von zur Gathen and Daniel Panario,Gauss periods and fast exponentiation in finite fields, in Lecture Notes in Computer Science, vol. 911, Springer-Verlag,  1995, 311--322.
  135. J. D. Key and F. E. Sullivan, Steiner triple systems with many affine hyperplanes, Congressus Numerant. 107 (1995), 105-112.
  136. L. L. Carpenter and J. D. Key, On Hadamard matrices from resolvable Steiner designs, Congressus Numerant. 108 (1995), 53-63.
  137.  Joel V. Brawley, Dedicated to Leonard Carlitz: The Man and his Work., Finite Fields and their Applications  1: 135-151 (1995).
    1994
  138. Shuhong Gao and Gary L. Mullen, Dickson polynomials and irreducible polynomials over finite fields, J. Number Theory  49 (1994), 118--132.
  139. Ian F. Blake, Shuhong Gao and Ronald C. Mullin, Normal and self-dual normal bases from factorization of cx q+1+dxq -ax -b, SIAM J. on Discrete Mathematics 7 (1994), 499-512.  PDF file (141k)
  140. Ian  F. Blake, Shuhong Gao and Robert L. Lambert, Constructive problems for irreducible polynomials over finite fields, in Information Theory and Applications (A. Gulliver and N. Secord, eds), LNCS 793, Springer-Verlag,  1994, 1-23.
  141. Shuhong Gao and Joachim von zur Gathen, Berlekamp's and Niederreiter's polynomial factorization algorithms, in Proc.  2nd International Conference on Finite Fields: Theory, Applications, and Algorithms, Las Vegas, 1993. Contemporary Mathematics, vol. 168,  1994, 101--116.
  142. J. D. Key and M. J. de Resmini, Codewords for projective planes from sets of type (s,t), European J. Combinatorics 15 (1994), 259-268.
  143. J. D. Key, Bases for codes of designs from finite geometries,  Congressus Numerantium 102 (1994), 33-44.
  144. J. D. Key, Ternary codes of Steiner triple systems, J. Combinatorial Designs 2 (1994), 25 - 30.
  145.  Joel V. Brawley, Preparing Mathematics Ph.D. Students for College Teaching  Careers Cultural Diversity and Change in Graduate Educatin:  Proceedings of the 1993 Conference of Southern Graduate Schools,  Jackson, Mississippi: pp 10-19 (1994).
  146.  Joel V. Brawley, Clemson University's Program for Preparing Mathematics Ph.D. Students for College Teaching Careers,  Chapter 7 of the book "So You're the Professor:  What Next", p.52-59. Mathematical Assoc. of America , 1994.
    1993
  147. Ian  F. Blake, Shuhong Gao and Ronald C. Mullin, Explicit factorization of x2^k +1 over Fp with prime $p \equiv 3 \bmod 4$, Applicable Algebra in Engineering, Communication and Computation 4 (1993), 89--94. PDF file (81k)
  148. Shuhong Gao and Wan-Di Wei, On non-Abelian group difference sets, Discrete Mathematics 123 (1993), 151-177. PDF file (107k)
  149. Wan-Di Wei, Shuhong Gao and Benfu Yang,Cyclic near difference sets of type 1, Discrete Mathematics 123 (1993), 151--177.
  150.  J. D. Key, On a class of 1-designs, European J. Combinatorics 14 (1993), 37 - 41.
  151.  J. D. Key and F. E. Sullivan, Codes of Steiner triple and quadruple systems, Des. Codes Cryptogr. 3 (1993), 117 - 125.
  152.  J. D. Key, Designs, codes and rigidity theorems,Congressus Numerantium, 95 (1993), 105-115.
  153.  Joel V. Brawley and Robert Jamison, Counting Transparent Strips of Numbers, Congressus Numerantium. 93: 143-148 (1993).
  154.  Joel V. Brawley, Remarks on the Professional Contributions of James L. (Vern)  Flatt - A Eulogy, The Mathmate (The Official Newsletter of the South  Carolina Council of Teachers of Mathematics), Vol. 16, No. 3, June 1993, p. 24, 40.
  155.  Joel V. Brawley and  Richard Millman, Labor and Management Issues in Drug Testing from a Probabilistic Viewpoint, Mathematics in College. Fall-Winter 1993; 30-42.
  156.  Joel V. Brawley, Polynomial Functions on Matrices over Finite Fields, Proceedings of the International Conference on Finite Fields, Coding Theory, and Advances in Communications and Computing.  Lecture Notes in Pure and Applied Mathematics, Marcel Dekker, Vol. 141: 15-31 (1993).
  157.  Joel V. Brawley and David Brown, Composed Products and Module Polynomials over Finite Fields, Discrete Mathematics 115:  41-56 (1993).
    1992
  158. Shuhong Gao and Hendrik W. Lenstra, Jr., Optimal normal bases, Designs, Codes and Cryptography 2 (1992), 315-323.  [More]
  159.  J. D. Key and K. Mackenzie, Ovals in the designs W(2m), Ars Combinatoria 33 (1992), 113-117.
  160.  E. F. Assmus, Jr.  and J. D. Key, Hadamard matrices and their designs: a coding-theoretic approach, Trans. Amer. Math. Soc. 330 (1992), 269-293.
  161.  J. D. Key, Extendable Steiner designs, Geometriae Dedicata 41 (1992), 201-205. 
  162.  Joel V. Brawley and Gary L. Mullen, Scalar polynomial functions on the nonsingular matrices over a finite field, LinearAlgebra Appl. 174 (1992), 1--12.
  163. Joel V. Brawley and Gary L. Mullen, Functions and polynomials over Galois rings, J. Number Theory 41 (1992), no. 2, 156--166.
  164.  Joel V. Brawley and Petr Lisonek,  Counting Equivalence Classes of Hadamard Pattern Sets by Group Action Methods, Research Institute for Symbolic Computation - Linz Report Series No. 92-93; 1-21 (May, 1992).
    1991 and earlier
  165. J. D. Key, Hermitian varieties as codewords, Designs, Codes and Cryptography 1 (1991), 255-259.
  166. J. D. Key and K. Mackenzie, On an upper bound for the p-rank of a translation plane, J. Combin. Theory (A),56 (1991), 297-302.
  167. Joel V. Brawley and David Brown, note on iterated presentations of algebraic extensions of finite fields, Proceedings of theTwenty-second Southeastern Conference on Combinatorics, Graph Theory, and Computing (Baton Rouge, LA, 1991). Congr. Numer. 85 (1991), 3--7.
  168. Joel V. Brawley and Gary L. Mullen, Infinite Latin squares containing nested sets of mutually orthogonal finite Latin squares, Publ. Math. Debrecen 39 (1991), no. 1-2, 135--141. 
  169. Joel V. Brawley, Clemson University's Doctoral Departments Project Site Report: Preparing the College Mathematics Teachers of the Future, Report 1 of the AMS-MAA-SIAM Committee on Preparation for College Teaching (editor B.A. Case). p.10-12 (1991).
  170. E. F. Assmus, Jr. and J. D. Key, Translation planes and derivation sets, J. Geometry, 37 (1990), 3 -16.
  171. E. F. Assmus, Jr.  and J. D. Key, Affine and projective planes, Discrete Math., 83 (1990), 161-187.
  172. E. F. Assmus, Jr.  and J. D. Key, Baer subplanes, ovals and unitals, In D. Ray-Chaudhuri, editor,  Coding Theory and Design Theory, pages 1-8, Springer-Verlag 1990. IMA Volumes in Mathematics and its Applications, Vol. 20.
  173. Wan-Di Wei, Shuhong Gao and Qing Xiang, On extraneous multipliers of Abelian difference sets, Combinatorial Designs and Applications} (Huangshan, 1988, W. D. Wallis, H. Shen, W. Wei, L. Zhu, Eds.), Marcel Dekker, Inc., 1990, 165--173.
  174. Shuhong Gao, On nonabelian group difference sets, Sichuan Daxue Xuebao 26 (1989), Special Issue, 136--139.
  175. J. D. Key and N. K. A. Rostom, A characterization of some finite inversive planes, Ars Combinatoria, 27 (1989), 193-196.
  176. E. F. Assmus, Jr. and J. D. Key, Arcs and ovals in hermitian and Ree unitals, European J. Combinatorics, 10 (1989), 297-308.
  177. Wan-Di Wei, Benfu Yang and Shuhong Gao, Distribution of values of permanent and standard forms of (0,1)-matrices,  Combinatorics and Graph Theory, Banach Center Publications, Warsaw,  25 (1989), 207--231. 
  178. Joel V. Brawley and Robert Gilmer, Fields that admit a nonlinear permutation polynomial, J. Algebra 123 (1989), no. 1, 111--119.
  179. Joel V. Brawley and L. Carlitz, A test for additive decomposability of irreducibles over a finite field, Discrete Math. 76 (1989), no. 1, 61--65.
  180. J. D. Key, Regular sets in geometries, Annals of Discrete Math., 37 (1988), 217-224.
  181. J. D. Key and N. K. A. Rostom, Unitary designs with regular sets, Discrete Math., 69 (1988), 235-239.
  182. Joel V. Brawley and L. Carlitz, Irreducibles and the composed product for polynomials over a finite field, Discrete Math. 65 (1987), no. 2, 115--139.
  183. Joel V. Brawley  and George E. Schnibben, Polynomials which permute the matrices over a field, Linear Algebra Appl. 86 (1987), 145--160.
  184. J. D. Key and J. Siemons, On the k-closure of finite linear groups, Bollettino U.M.I. (7), 1-B (1987), 31-55.
  185. J. D. Key and J. Siemons, Regular sets and geometric groups, Resultate Math., 11 (1987), 97-116.
  186. J. D. Key, J. Siemons and A. Wagner, Regular sets on the projective line, J. Geometry, 27 (1986), 188-194. 
  187. E. F. Assmus, Jr.  and J. D. Key, On an infinite class of Steiner systems with t=3 and k=6, J. Combin. Theory (A), 42 (1986), 55-60. 
  188. G. A. Kadir and J. D. Key, The Steiner system S(5,8,24) constructed from dual affine planes, Proc. Roy. Soc. Edinburgh, 103A (1986), 147-160. 
  189. J. D. Key and J. Siemons, Closure properties of the special linear groups, Ars Combin., 22 (1986), 107-117. 
  190. J. D. Key and A. Wagner, On an infinite class of Steiner systems constructed from affine spaces, Arch. Math., 47 (1986), 376-378. 
  191. J. D. Key, On the p-rank of t-designs, Proc. 29th Midwest Symposium on Circuits and Systems, University of Nebraska-Linclon, Elsevier (1986), 961-964.
  192. Joel V. Brawley, Vandermonde independent matrices, basic sets, and polynomial matrix functions over a finite field, Linear and Multilinear Algebra 19 (1986), no. 4, 373--386.
  193. J. D. Key and E. E. Shult, Steiner triple systems with doubly-transitive automorphism groups, J. Combin. Theory  (A), 36 (1984), 105-110. 
  194. W. N. Everitt and J. D. Key, On some properties of matrices associated with linear ordinaryquasi-differential expressions, Proc. Roy. Soc. Edinburgh, 96A (1984), 211-220.
  195. J. D. Key, A note on a consequence for affine groups of the classification theorem of finite simple groups, Geom. Ded., 14 (1983), 81-86.
  196. Joel V. Brawley, Counting matrices by Drazin index, SIAM J. Algebraic Discrete Methods 3 (1982), no. 1, 30--34.
  197. Joel V. Brawley and Max Hankins, On distribution by rank of bases for vector spaces of matrices over a finite field, Linear Algebra Appl. 39 (1981), 91--101.
  198. Joel V. Brawley and Gary L. Mullen, A note of equivalence classes of matrices over a finite field, Internat. J. Math. Math. Sci. 4 (1981), no. 2, 279--287.
  199. Joel V. Brawley, A note on polynomial matrix functions over a finite field, Linear Algebra Appl. 28 (1979), 35--38.
  200. J. D. Key, Some maximal subgroups of certain unimodular groups, J. London Math. Soc. (2), 19 (1979), 291-300.
  201. Joel V. Brawley and R. O. Gamble, Involutory matrices over finite commutative rings, Linear Algebra Appl. 21 (1978), no. 2,175--188.
  202.  Joel V. Brawley and Jack Levine, Equivalences of Vigenere Systems over Finite Groups, Crytologia, Vol. 1, No. 4 (1977), 338-361.
  203. Joel V. Brawley and Paul Duvall, Some Roots of the J-Matrix, R51 Technical Report, NSA (1977).
  204. Joel V. Brawley and Jack Levine, Some Cryptographic Applications of Permutation Polynomials, Cryptologia, Vol. 1, No. 1 (1977), 76-92.
  205. Joel V. Brawley, The number of polynomial functions which permute the matrices over a finite field, J. Combinatorial Theory Ser. A 21 (1976), no. 2, 147--154.
  206. Joel V. Brawley, Polynomials over a ring that permute the matrices over that ring,  J. Algebra 38 (1976), no. 1, 93--99.
  207. Edward A. Bender and Joel V. Brawley, Similarity to symmetric matrices over fields which are not formally real, Collection of articles dedicated to Olga Taussky-Todd. Linear and Multilinear Algebra 3 (1975/76), no. 1/2, 3--8.
  208. Joel V. Brawley,  L. Carlitz and Jack Levine,  Scalar polynomial functions on the n x n matrices over a finite field, Linear Algebra and Appl. 10 (1975), 199--217. 
  209. J. D. Key, Some maximal subgroups of $PSL_n(q)$,  $n \geq 3$, $q=2^r$, Geom. Ded., 4 (1975), 377-386.
  210. Joel V. Brawley, L. Carlitz and J. Levine, Power sums of matrices over a finite field, Duke Math. J. 41 (1974), 9--24.
  211. Joel V. Brawley, L. Carlitz and TheresaVaughan, Linear permutation polynomials with coefficients in a subfield, Collection of articles dedicated to Carl Ludwig Siegel on the occasion of his seventy-fifth birthday, II. Acta Arith. 24 (1973), 193--199.
  212. Joel V. Brawley and L. Carlitz, An addendum to the paper: A characterization of the n x n matrices over a finite field, (Amer. Math. Monthly {80} (1973), 670--672). Amer. Math. Monthly 80 (1973), 1041--1043.
  213. Joel V. Brawley and L. Carlitz, A characterization of the n x n matrices over a finite field, Amer. Math. Monthly 80 (1973), 670--672.
  214. Joel V. Brawley and L. Carlitz, Enumeration of matrices with prescribed row and column sums, Linear Algebra and Appl. 6 (1973), 165--174.
  215. Joel V. Brawley and Jack Levine, Equivalence classes of involutory mappings, Duke Math. J. 39 (1972), 211--217.
  216. Joel V. Brawley and Jack Levine, Equivalence classes of linear mappings with applications to algebraic cryptography I, Duke Math. J. 39 (1972), 121--132.
  217. Joel V. Brawley and Jack Levine, Equivalence classes of linear mappings with applications to algebraic cryptography II, Duke Math. J. 39 (1972), 133--142.
  218. Joel V. Brawley, On the ranks of bases of vector spaces of matrices, Linear Algebra and Appl. 3 (1970) 51--55.
  219. Joel V. Brawley, Certain sets of involutary matrices and their groups, Duke Math. J. 36 (1969) 473--478.
  220. J. D. King, Doubly transitive groups in which involutions fix one or three points, Math. Z., 111 (1969), 311-321.
  221. J. D. King, Correction to A characterization of some doubly transitive groups, Math. Z., 112 (1969), 393-394.
  222. J. D. King, A characterization of some doubly transitive groups, Math. Z., 107 (1968), 43-48.
  223. Joel V. Brawley, Similar involutory matrices modulo R, Duke Math. J. 34 (1967) 649--665.
  224. Joel V. Brawley,  Enumeration of canoncical sets by rank, Amer. Math. Monthly 74 (1967) 175--177. 
  225. Jack Levine and Joel V. Brawley, Involutory commutants with some applications to algebraic cryptography, II,  J. ReineAngew. Math. 227 (1967), 1--24.
  226. Jack Levine and Joel V. Brawley, Involutory commutants with some applications to algebraic cryptography, I,  J. ReineAngew. Math.  224 (1966), 20--43.
  227. Joel V. Brawley,  Similar involutory matrices (mod p^m), Amer. Math. Monthly 73 (1966) 499--501.


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