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 Applicable Algebra Lab

Publications

         Books
      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

 
 
 

 
  1. 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)
  2. 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)
  3. 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)
  4. 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)
  5. Shuhong Gao and D. Frank Hsu, ``Short containers in Cayley graphs'',  DIMACS tech report 2001-18, May 2001. (15 pages) PS file (336K) or PDF file (135K)
  6. Shuhong Gao, ``Factoring multivariate polynomials via partial differential equations,''  Mathematics of Computation 72 (2003), 801--822. PS file (502K) or PDF file (201K)
  7. Shuhong Gao and Alan G.B. Lauder, ``Hensel lifting and polynomial factorisation,'' Mathematics of Computation 71 (2002), 1663-1676). [More]
  8. J. D. Key, J. Moori and B.~G. Rodrigues, ``Some binary codes with automorphism group containing the symplectic group of odd characteristic''. (In preparation.) 
  9. J.~D. Key, J. Moori and B.~G. Rodrigues, ``Binary codes of triangular graphs and permutation decoding''.(In preparation.)
  10. J. D. Key and J. Moori, ``Designs, codes and graphs from the Janko groupsJ 1 and J2'', J. Combin. Math. & Combin. Comput. (To appear)
  11. Peng Ding and Jennifer D. Key, ``Subcodes of projective generalized Reed-Muller codes spanned by  minimum-weight vectors'', Des. Codes Cryptogr. (To appear)
  12. K. L. Clark and J. D. Key and M. J. de Resmini, ``Dual codes of translation planes''.  (Submitted)
  13. J. D. Key and M. J. de Resmini, ``An upper bound for the minimum weight of dual codes of Figueroa planes''. (Submitted)
  14. J. D. Key, J. Moori and B. G. Rodrigues, ``On some designs and codes from primitive representations of some finite simple groups'', J. Combin. Math.& Combin. Comput. (to appear).
  15. 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)


    16. 2001
  16. 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)
  17. 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)
  18. Shuhong Gao, ``Absolute irreducibility of polynomials via Newton polytopes,'' J. of Algebra 237 (2001), 501--520. gzipped PS file (502K) or PDF file (200K)
  19. Shuhong Gao, ``On the deterministic complexity of polynomial factoring,'' J. Symbolic Computation 31 (2001), 19--36. [More] 
  20. 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)
  21.  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.
  22.  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.
    2000
  23. 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)
  24. 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)
  25.  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.
  26.  Peng Ding and Jennifer D. Key, ``Minimum-weight codewords as generators of generalized Reed-Muller codes'', IEEE Trans. Inform. Theory 46 (2000), 2152 -- 2158.
  27.  Joel V. Brawley, ``In Memoriam:  Leonard Carlitz (1907-1999)'',  Finite Fields and Their Applications 6: 203-206 (2000).
    1999
  28. Shuhong Gao, ``Elements of provable high orders in finite fields,'' Proc. American Math. Soc. 127  (1999), 1615--1623. PDF file (153K)
  29. 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)
  30. 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)
  31. 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. 
  32.  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. 
  33. J.  D. Key and F. E. Sullivan, ``Steiner systems from binary codes'', Ars Combin. 52 (1999), 153--159.
  34. K. L. Clark and J. D. Key, ``Geometric codes over fields of odd prime power order'', Congr. Numer. 137 (1999), 177 - 186.
  35. J. V. Brawley and T. Mateer, ``Video Poker in South Carolina: A Mathematical Study'', The SC Digest, Strom Thurmond Institute, Clemson University, 1999.

    36. 1998
  36. 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)
  37. 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)
  38. 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)
  39. J. D. Key, ``Codes and finite geometries'', Congr. Numer. 131 (1998), 85--99. 
  40. J. D. Key and M. J. de Resmini,  ``Small sets of even type and codewords'', J. Geom. 61 (1998), 83--104.
  41. J. V. Brawley and T. Teitloff, ``Similarity to Symmetric Matrices over Finite Fields'', Finite Fields and Applications 4 (1998),  261-274.
    1997
  42. Shuhong Gao and Daniel Panario, ``Density of normal elements,'' Finite Fields and Their Applications  3 (1997), 141--150. PS file (169k)
  43. 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)
  44. 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)
  45.  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).
  46.  J. D. Key, B. Novick, and F. E. Sullivan, ``Binary codes of structures dual to unitals'', Congr. Numer. 123 (1997), 119--124.
  47.  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
  48. 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)
  49. E. F. Assmus, Jr. and J. D. Key, ``Designs and codes: an update'', Des. Codes Cryptogr., 9 (1996), 7-27.
  50. L. L. Carpenter and J. D. Key, ``Oval designs and Reed-Muller codes'', J. Combin. Math. & Combin. Comput.,22 (1996), 79-85.
  51. J. D. Key, ``Extendable Steiner designs from finite geometries'', J. Statist. Plann.  Inference, 56 (1996), 181-186.
    1995
  52. Shuhong Gao and Scott A. Vanstone, ``On orders of optimal normal basis generators,'' Mathematics of Computation  64 (1995), 1227--1233.  PDF file (92k)
  53. 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.
  54. J. D. Key and F. E. Sullivan, ``Steiner triple systems with many affine hyperplanes'', Congressus Numerant. 107 (1995), 105-112.
  55. L. L. Carpenter and J. D. Key, ``On Hadamard matrices from resolvable Steiner designs'', Congressus Numerant. 108 (1995), 53-63.
  56.  Joel V. Brawley, ``Dedicated to Leonard Carlitz: The Man and his Work.'', Finite Fields and their Applications  1: 135-151 (1995).
    1994
  57. Shuhong Gao and Gary L. Mullen, ``Dickson polynomials and irreducible polynomials over finite fields,'' J. Number Theory  49 (1994), 118--132.
  58. 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)
  59. 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.
  60. 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.
  61. 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.
  62. J. D. Key, ``Bases for codes of designs from finite geometries'',  Congressus Numerantium 102 (1994), 33-44.
  63. J. D. Key, ``Ternary codes of Steiner triple systems'', J. Combinatorial Designs 2 (1994), 25 - 30.
  64.  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).
  65.  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
  66. 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)
  67. Shuhong Gao and Wan-Di Wei, ``On non-Abelian group difference sets,'' Discrete Mathematics 123 (1993), 151-177. PDF file (107k)
  68. Wan-Di Wei, Shuhong Gao and Benfu Yang,``Cyclic near difference sets of type 1,'' Discrete Mathematics 123 (1993), 151--177.
  69.  J. D. Key, ``On a class of 1-designs'', European J. Combinatorics 14 (1993), 37 - 41.
  70.  J. D. Key and F. E. Sullivan, ``Codes of Steiner triple and quadruple systems'', Des. Codes Cryptogr. 3 (1993), 117 - 125.
  71.  J. D. Key, ``Designs, codes and rigidity theorems'',Congressus Numerantium, 95 (1993), 105-115.
  72.  Joel V. Brawley and Robert Jamison, ``Counting Transparent Strips of Numbers'', Congressus Numerantium. 93: 143-148 (1993).
  73.  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.
  74.  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.
  75.  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).
  76.  Joel V. Brawley and David Brown, ``Composed Products and Module Polynomials over Finite Fields'', Discrete Mathematics 115:  41-56 (1993).
    1992
  77. Shuhong Gao and Hendrik W. Lenstra, Jr., ``Optimal normal bases,'' Designs, Codes and Cryptography 2 (1992), 315-323.  [More]
  78.  J. D. Key and K. Mackenzie, ``Ovals in the designs W(2m)'', Ars Combinatoria 33 (1992), 113-117.
  79.  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.
  80.  J. D. Key, ``Extendable Steiner designs'', Geometriae Dedicata 41 (1992), 201-205. 
  81.  Joel V. Brawley and Gary L. Mullen, ``Scalar polynomial functions on the nonsingular matrices over a finite field'', LinearAlgebra Appl. 174 (1992), 1--12.
  82. Joel V. Brawley and Gary L. Mullen, ``Functions and polynomials over Galois rings'', J. Number Theory 41 (1992), no. 2, 156--166.
  83.  Joel V. Brawley and Petr Lisonek,  ``Counting Equivalence Classes of Hadamard Pattern Sets by 

    84. Group Action Methods'', Research Institute for Symbolic Computation - Linz Report Series No. 92-93; 1-21 (May, 1992).
    Up to 1991
  84. J. D. Key, ``Hermitian varieties as codewords'', Designs, Codes and Cryptography 1 (1991), 255-259.
  85. 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.
  86. 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.
  87. 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. 
  88. 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).
  89. E. F. Assmus, Jr. and J. D. Key, ``Translation planes and derivation sets'', J. Geometry, 37 (1990), 3 -16.
  90. E. F. Assmus, Jr.  and J. D. Key, ``Affine and projective planes'', Discrete Math., 83 (1990), 161-187.
  91. 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.
  92. 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.
  93. Shuhong Gao, ``On nonabelian group difference sets,'' Sichuan Daxue Xuebao 26 (1989), Special Issue, 136--139.
  94. J. D. Key and N. K. A. Rostom, ``A characterization of some finite inversive planes'', Ars Combinatoria, 27 (1989), 193-196.
  95. E. F. Assmus, Jr. and J. D. Key, ``Arcs and ovals in hermitian and Ree unitals'', European J. Combinatorics, 10 (1989), 297-308.
  96. 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. 
  97. Joel V. Brawley and Robert Gilmer, ``Fields that admit a nonlinear permutation polynomial'', J. Algebra 123 (1989), no. 1, 111--119.
  98. 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.
  99. J. D. Key, ``Regular sets in geometries'', Annals of Discrete Math., 37 (1988), 217-224.
  100. J. D. Key and N. K. A. Rostom, ``Unitary designs with regular sets'', Discrete Math., 69 (1988), 235-239.
  101. 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.
  102. Joel V. Brawley  and George E. Schnibben, ``Polynomials which permute the matrices over a field'', Linear Algebra Appl. 86 (1987), 145--160.
  103. J. D. Key and J. Siemons, ``On the k-closure of finite linear groups'', Bollettino U.M.I. (7), 1-B (1987), 31-55.
  104. J. D. Key and J. Siemons, ``Regular sets and geometric groups'', Resultate Math., 11 (1987), 97-116.
  105. J. D. Key, J. Siemons and A. Wagner, ``Regular sets on the projective line'', J. Geometry, 27 (1986), 188-194. 
  106. 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. 
  107. 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. 
  108. J. D. Key and J. Siemons, ``Closure properties of the special linear groups'', Ars Combin., 22 (1986), 107-117. 
  109. J. D. Key and A. Wagner, ``On an infinite class of Steiner systems constructed from affine spaces'', Arch. Math., 47 (1986), 376-378. 
  110. 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.
  111. 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.
  112. J. D. Key and E. E. Shult, ``Steiner triple systems with doubly-transitive automorphism groups'', J. Combin. Theory  (A), 36 (1984), 105-110. 
  113. 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.
  114. 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.
  115. Joel V. Brawley, ``Counting matrices by Drazin index'', SIAM J. Algebraic Discrete Methods 3 (1982), no. 1, 30--34.
  116. 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.
  117. 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.
  118. Joel V. Brawley, ``A note on polynomial matrix functions over a finite field'', Linear Algebra Appl. 28 (1979), 35--38.
  119. J. D. Key, ``Some maximal subgroups of certain unimodular groups'', J. London Math. Soc. (2), 19 (1979), 291-300.
  120. Joel V. Brawley and R. O. Gamble, ``Involutory matrices over finite commutative rings'', Linear Algebra Appl. 21 (1978), no. 2,175--188.
  121.  Joel V. Brawley and Jack Levine, ``Equivalences of Vigenere Systems over Finite Groups'', Crytologia, Vol. 1, No. 4 (1977), 338-361.
  122. Joel V. Brawley and Paul Duvall, ``Some Roots of the J-Matrix'', R51 Technical Report, NSA (1977).
  123. Joel V. Brawley and Jack Levine, ``Some Cryptographic Applications of Permutation Polynomials'', Cryptologia, Vol. 1, No. 1 (1977), 76-92.
  124. 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.
  125. Joel V. Brawley, ``Polynomials over a ring that permute the matrices over that ring'',  J. Algebra 38 (1976), no. 1, 93--99.
  126. 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.
  127. 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. 
  128. J. D. Key, ``Some maximal subgroups of $PSL_n(q)$,  $n \geq 3$, $q=2^r$'', Geom. Ded., 4 (1975), 377-386.
  129. Joel V. Brawley, L. Carlitz and J. Levine, ``Power sums of matrices over a finite field'', Duke Math. J. 41 (1974), 9--24.
  130. 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.
  131. 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.
  132. 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.
  133. Joel V. Brawley and L. Carlitz, ``Enumeration of matrices with prescribed row and column sums'', Linear Algebra and Appl. 6 (1973), 165--174.
  134. Joel V. Brawley and Jack Levine, ``Equivalence classes of involutory mappings'', Duke Math. J. 39 (1972), 211--217.
  135. Joel V. Brawley and Jack Levine, ``Equivalence classes of linear mappings with applications to algebraic cryptography I'', Duke Math. J. 39 (1972), 121--132.
  136. Joel V. Brawley and Jack Levine, ``Equivalence classes of linear mappings with applications to algebraic cryptography II'', Duke Math. J. 39 (1972), 133--142.
  137. Joel V. Brawley, ``On the ranks of bases of vector spaces of matrices'', Linear Algebra and Appl. 3 (1970) 51--55.
  138. Joel V. Brawley, ``Certain sets of involutary matrices and their groups'', Duke Math. J. 36 (1969) 473--478.
  139. J. D. King, ``Doubly transitive groups in which involutions fix one or three points'', Math. Z., 111 (1969), 311-321.
  140. J. D. King, Correction to ``A characterization of some doubly transitive groups'', Math. Z., 112 (1969), 393-394.
  141. J. D. King, ``A characterization of some doubly transitive groups'', Math. Z., 107 (1968), 43-48.
  142. Joel V. Brawley, ``Similar involutory matrices modulo R'', Duke Math. J. 34 (1967) 649--665.
  143. Joel V. Brawley,  ``Enumeration of canoncical sets by rank'', Amer. Math. Monthly 74 (1967) 175--177. 
  144. Jack Levine and Joel V. Brawley, ``Involutory commutants with some applications to algebraic cryptography, II'',  J. ReineAngew. Math. 227 (1967), 1--24.
  145. Jack Levine and Joel V. Brawley, ``Involutory commutants with some applications to algebraic cryptography, I'',  J. ReineAngew. Math.  224 (1966), 20--43.
  146. Joel V. Brawley,  ``Similar involutory matrices (mod p^m)'', Amer. Math. Monthly 73 (1966) 499--501.

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