J. D. Key
Jennifer D. Key
BSc(Hons) (Rand) MPhil PhD (Lond)
Professor of Mathematical Sciences,
Department of Mathematical Sciences, Clemson University.
Research Interests:
Finite geometries, combinatorial designs,
error-correcting codes, and groups. See also
Applicable Algebra Laboratory.
Sample Publications:
- ``Designs and Their Codes," joint with E. F. Assmus, Jr, 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)
-
``Hermitian varieties as codewords,"
Designs, Codes and Cryptography, 1 (1991), 255-259
- ``Ternary codes of Steiner triple systems," J. Combinatorial Designs,
2 (1994), 25-30.
- ``Hadamard matrices and their designs: a coding-theoretic approach,"
joint with E. F. Assmus, Jr,
Trans. Amer. Math. Soc, 330 (1992), 269-293.
- ``Codewords for projective planes from sets of type (s,t),"
joint with M. J. de Resmini,
European J. Combinatorics, 15 (1994), 259-268
-
``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)
- ``Some applications of Magma in designs and codes",
J. Symbolic Comput., Special Issue (To appear.)
(
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 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)
- ``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.
- ``Ternary dual codes of the planes of order nine",
joint with M. J. de~Resmini,
J. Statist. Plann. Inference, To appear.
(
View)
Sadly, Ed Assmus died recently. See his
obituary . See also
(DCC web site)
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:
J. D. Key, Department of Mathematical Sciences,
Clemson University, Clemson, SC 29634
Tel: (864) 656 5226 or 3434
Fax: (864) 656 5230
email: keyj@math.clemson.edu
Home page: http://www.math.clemson.edu/faculty/Key