J. D. Key

Jennifer D. Key BSc(Hons) (Rand) MPhil PhD (Lond)
Professor Emeritus of Mathematical Sciences, School of Mathematical and Statistical Sciences, Clemson University.
Honorary Professor Aberystwyth University or IMPACS Aberystwyth, University of KwaZulu-Natal, University of the Western Cape.

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 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, Advanmath 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
• Recent developments in permutation decoding, Notices of the South African Mathematical Society, April (2006) 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., 30 (2009), 220--229 View
• Minimum words of codes from affine planes, joint with D. Ghinelli and M. J. de Resmini, J. Geom. 91 (2008), 43-51 View
• Graphs, designs and codes related to the n-cube, joint with W. Fish and E. Mwambene, Discrete Math. 309 (2009), 3255-3269 View
• Binary codes from the line graph of the n-cube, joint with W. Fish and E. Mwambene, J. Symbolic Comput. 45 (2010) 800--812 View
• Codes associated with triangular graphs, and permutation decoding, joint with J. Moori and B. Rodrigues, Int. J. Information and Coding Theory, Vol. 1, No. 3, (2010), 334-349 View
• Codes from lattice and related graphs, and permutation decoding, joint with B. Rodrigues, Discrete Appl. Math., Vol. 158, (2010), 1807-1815 View
• Codes from incidence matrices and line graphs of Paley graphs, joint with Dina Ghinelli, Adv. Math. Commun., Vol. 5, (2011), 93--108 View
• Codes from incidence matrices of graphs, joint with P. Dankelmann and B.G. Rodrigues, Des. Codes Crytogr., Vol. 68, (2013), 393-393 View , Online
• Hulls of codes from incidence matrices of connected regular graphs, joint with Dina Ghinelli and T. P. McDonough, Des. Codes Crytogr., Vol. 70 (2014), 35-54 View , Online
• Partial permutation decoding for simplex codes, joint with W. Fish and E. Mwambene, Adv. Math. Commun., Vol. 6, (2012), 505-516 View , Online
• A characterization of graphs by codes from their incidence matrices, joint with P. Dankelmann and B.G. Rodrigues, Electron. J. Combinatorics 20(3) (2013), #P18 View
• Codes associated with the odd graphs, joint with W. Fish and E. Mwambene, Discrete Math. 315-316 (2014), 102-111 View
• Codes from Hall planes of even order, joint with T.P. McDonough and V.C. Mavron, J. Geom. 105 (2014), 33-41 View
• Binary codes from reflexive graphs on 3-sets, joint with W. Fish and E. Mwambene, Adv. Math. Commun. 9 (2015), 211-232 View
• Partial permutation decoding for MacDonald codes, joint with P. Seneviratne, Appl. Algebra Engrg. Comm. Comput. 27 (2016), 399-412 View
• Improved partial permutation decoding for Reed-Muller codes, joint with T.P. McDonough and V.C. Mavron, Discrete Math. 340 (2017), 722-728 View
• LCD codes from adjacency matrices of graphs, joint with B. G. Rodrigues, Appl. Algebra Engrg. Comm. Comput. 29 (3) (2018), 227-244
  DOI: 10.1007/s00200-017-0339-6 View
• Special LCD codes from Peisert and generalized Peisert graphs, joint with B. G. Rodrigues, Graphs Combin. 35 (2019), 633-652
  DOI: https://doi.org/10.1007/s00373-019-02019-0 View
• Binary codes from $m$-ary $n$-cubes $Q^m_n$, joint with B. G. Rodrigues, Adv. Math. Commun.
  DOI: https://doi:10.3934/amc.2020079 View
• Special LCD codes from products of graphs, joint with W. Fish and E. Mwambene, Appl. Algebra Engrg. Comm. Comput.
  DOI: https://doi.org/10.1007/s00200-021-00517-4 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 and RMcodes and basis set
• 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
• Simplex codes (2011)
  simplex and a run for n=6 at simp6LOG ; 31 matrimath for a 30-PD-set for S_8 sim8_31.m ; Field extension construction: ext_field.m
• Peisert graph decoding
  P49.m and a run run49.txt

email: keyj@clemson.edu

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