J. D. Key

Jennifer D. Key BSc(Hons) (Rand) MPhil PhD (Lond)
Professor Emeritus of Mathematical Sciences, Department of Mathematical Sciences, Clemson University.

Research Interests:

Sample Publications:

• ``Designs and Their Codes," joint with E. F. Assmus, Jr ( obituary ), Cambridge University Press Tracts in Mathematics, No. 103, 1992. ( View Table of Contents and Preface. View errata files: 1992 (first printing) or 1993 (second printing).) (CUP web site)
• Designs and codes: an update, joint with E. F. Assmus, Jr, Designs, Codes and Cryptography, 9 (1996), 7-27 View or see ( DCC web site) or for the table of contents, View
• Computational results for the known biplanes of order 9, joint with V.D. Tonchev, 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), 113-122. View
• Codes and finite geometries, joint with E. F. Assmus, Jr, INRIA Report, No. 2027, September 1993 (88 pages) ( View Table of Contents and Introduction) or read (ps) or read (pdf) chapter joint with E. F. Assmus, Jr., on ``Polynomial Codes and Finite Geometries" in ``Handbook of Coding Theory", Volume 2, Chapter 16, pages 1269--1343, edited by V.S. Pless and W.C. Hufffman (Elsevier, 1998)
• Small sets of even type and codewords, joint with M. J. de Resmini, J. Geom., 61 (1998), 83--104 View
• Bases of minimum-weight vectors for codes from designs, joint with S. Gao, Finite Fields and their Applications, 4 (1998) 1-15 View
• Minimum weight and dimension formulas for some geometric codes, joint with Neil J. Calkin and Marialuisa J. de Resmini, Des. Codes Cryptogr., 17 (1999), 105--120, View and to view some polynomial functions giving the dimension of the dual code of the design of points and subspaces of dimension r over the field of order q, as described in this paper, see polynomials and more.
• Some error-correcting codes and their applications, Chapter 19 of ``Applied Mathematical Modeling: A Multidisciplinary Approach", D. R. Shier and K. T. Wallenius (Eds.), CRC Press, Boca Raton, FL, 1999 View
• Geometric codes over fields of odd prime power order, joint with K. L. Clark , Congr. Numer. 137 (1999), 177 - 186 View
• Rigidity theorems for a class of affine resolvable designs, joint with K. Mackenzie Fleming, J. Combin. Math. & Combin. Comput. 35 (2000), 147--160 View
• Ternary dual codes of the planes of order nine, joint with M. J. de Resmini, J. Statist. Plann. Inference, 95 (2001), 229 -- 236 View
• Minimum-weight codewords as generators of generalized Reed-Muller codes, joint with Peng Ding, IEEE Trans. Inform. Theory, 46 (2000), 2152 --2158 View
• Some applications of Magma in designs and codes, J. Symbolic Comput., 31 (2001), 37-53 View
• Subcodes of projective generalized Reed-Muller codes spanned by minimum-weight vectors, joint with Peng Ding, Des. Codes Cryptogr., 26 (2002), 197--211 View
• Codes, designs and groups from the Janko groups J1 and J2, joint with J. Moori, J. Combin. Math. & Combin. Comput. 40 (2002), 143--159 View
• Dual codes of translation planes, joint with K. L. Clark and M. J. de Resmini, European J. Combin., 23 (2002), 529--538 View
• Dual codes of projective planes of order 25, joint with K. L. Clark, L. D. Hatfield and H. N. Ward, Advances in Geometry, 3 (2003) Special Issue, 140--152 View
• Permutation decoding for the binary codes from triangular graphs, joint with J. Moori and B.G. Rodrigues, European J. Combin., 25 (2004), 113--123 View
• Binary codes from graphs on triples, joint with J. Moori and B.G. Rodrigues, Discrete Math., 282 (2004), 171--182 View
• Binary codes from graphs on triples and permutation decoding, joint with J. Moori and B.G. Rodrigues, Ars Combin., 79 (2006), 11--19 View
• Partial permutation decoding for codes from finite planes, joint with T.P. McDonough and V.C. Mavron, European J. Combin., 26 (2005), 665--682 View
• Partial permutation decoding for codes from Paley graphs, joint with J. Limbupasiriporn, Congr. Numer. 170 (2004), 143--155 View
• Information sets and partial permutation decoding for codes from finite geometries, joint with T.P. McDonough and V.C. Mavron, Finite Fields Applic., 12 (2006), 232--247 View
• Binary codes from rectangular lattice graphs and permutation decoding, joint with P. Seneviratne, European J. Combin., 28 (2007), 121--126 View
• An upper bound for the minimum weight of the dual codes of desarguesian planes, joint with T.P. McDonough and V.C. Mavron, European J. Combin. (To appear) View

Some designs from my Magma files:

• Projective planes of order 9: Hughes , derived (Hall) , dual derived .
• Projective planes of order 25: Hughes ;
  translation planes: derived (Hall), S3, S4, S5, A1, A2, A3, A4, A5, A6, A7, A8, B1, B2, B3, B4, B5, B6, B7, B8.
• Biplanes on 56 points: biplanes .
• Dimension of code of finite geometry design: Magma functions .
• Some symmetric designs with parameters of finite geometry designs:
  rank and group , designs , extended designs , sample run .
• Affine resolvable 2-(27,9,4) designs of Lam and Tonchev:
  weight distribution for 68 dual designs , designs 2-9 , designs 10-19 , designs 20-29 , designs 30-39, designs 40-49, designs 50-59 , designs 60-68 .
• Janko groups and designs: codes or J1 or J2 . New (2007/8): Codes from the Janko groups: 2008 (text) or pdf . A 6-PD-set of size 404 for J2 on [100,36,16] binary code: 6-PD-set.
• PD-sets for some codes:
  [126,56,6] or [126,70,5] or [126,78,5] and more .
• Tame search (Rome 2008)
  BBH1_16 BBH2_17 BBS4_21 DBBH2_18 DBBS4_22 DDEMP_9 DDSF_13 DEMP_8 DHALL_5 DJOHN_20 DJOWK_7 DLMRH_11 DMATH_15 DSFP_12 HALL_4 JOHN_19 JOWK_6 LMRH_10 MATH_14 SEMI2_2 SEMI4_3 Hughes9.m Hall9.m DHall9.m

Tel: (864) 656 3434

email: keyj@ces.clemson.edu or keyj@clemson.edu

Home page: http://www.ces.clemson.edu/~keyj