On circulant self-dual codes over small fields

被引：27

作者：

Grassl, Markus ^{[1
,2
]}

Gulliver, T. Aaron ^{[3
]}

机构：

[1] Univ Karlsruhe TH, Fak Informat, Inst Algorithmen & Kognit Syst IAKS, D-76128 Karlsruhe, Germany

[2] Austrian Acad Sci, Inst Quantum Opt & Quantum Informat IQOQI, A-6020 Innsbruck, Austria

[3] Univ Victoria, Dept Elect & Comp Engn, STN CSC, Victoria, BC V8W 3P6, Canada

来源：

DESIGNS CODES AND CRYPTOGRAPHY | 2009年 / 52卷 / 01期

关键词：

Self-dual codes; Circulant codes; Bounds on codes; MDS;

D O I：

10.1007/s10623-009-9267-1

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We construct self-dual codes over small fields F-q with q = 3, 4, 5, 7, 8,9 of moderate length with long cycles in the automorphism group. With few exceptions, the codes achieve or improve the known lower bounds on the minimum distance of self-dual codes.

引用

页码：57 / 81

页数：25

共 36 条

[1] [Anonymous], 1978, The Theory of Error-Correcting Codes
[2] Self-dual codes over F3 and negacirculant conference matrices
Arasu, K. T.
Chen, Yu Qing
Gulliver, T. Aaron
Song, Weilai
[J]. 2006 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY, VOLS 1-6, PROCEEDINGS, 2006, : 1301 - +
[3] Assmus E. F. Jr., 1972, Discrete Mathematics, V3, P1, DOI 10.1016/0012-365X(72)90021-0
[4] Beenker G. F. M., 1984, IEEE Transactions on Information Theory, VIT-30, P403, DOI 10.1109/TIT.1984.1056859
[5] The Magma algebra system .1. The user language
Bosma, W
Cannon, J
Playoust, C
[J]. JOURNAL OF SYMBOLIC COMPUTATION, 1997, 24 (3-4) : 235 - 265
[6] Brouwer AE, 1998, HANDBOOK OF CODING THEORY, VOLS I & II, P295
[7] Quadratic double circulant codes over fields
Gaborit, P
[J]. JOURNAL OF COMBINATORIAL THEORY SERIES A, 2002, 97 (01) : 85 - 107
[8] Experimental constructions of self-dual codes
Gaborit, P
Otmani, A
[J]. FINITE FIELDS AND THEIR APPLICATIONS, 2003, 9 (03) : 372 - 394
[9] Gaborit P., Tables of Self-Dual Codes
[10] GABORIT P, 2000, IEEE T INFORM THEORY, V54, P3865

← 1 2 3 4 →