Self-dual codes over commutative Frobenius rings

被引：83

作者：

Dougherty, Steven T. ^{[2
]}

Kim, Jon-Lark ^{[1
]}

Kulosman, Hamid ^{[1
]}

Liu, Hongwei ^{[3
]}

机构：

[1] Univ Louisville, Dept Math, Louisville, KY 40292 USA

[2] Univ Scranton, Dept Math, Scranton, PA 18510 USA

[3] Huazhong Normal Univ, Dept Math, Wuhan 430079, Hubei, Peoples R China

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2010年 / 16卷 / 01期

关键词：

Self-dual codes; Codes over rings; WEIGHT ENUMERATORS; CODING THEORY; FINITE RINGS; MDS CODES; EQUIVALENCE; MODULES;

D O I：

10.1016/j.ffa.2009.11.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that self-dual codes exist over all finite commutative Frobenius rings, via their decomposition by the Chinese Remainder Theorem into local rings. We construct non-free self-dual codes under some conditions, using self-dual codes over finite fields, and we also construct free self-dual codes by lifting elements from the base finite field. We generalize the building-up construction for finite commutative Frobenius rings, showing that all self-dual codes with minimum weight greater than 2 can be obtained in this manner in cases where the construction applies. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：14 / 26

页数：13

共 19 条

[1] WEIGHT ENUMERATORS OF SELF-DUAL CODES [J].

BRUALDI, RA ;

PLESS, VS .

IEEE TRANSACTIONS ON INFORMATION THEORY, 1991, 37 (04) :1222-1225

[2] On the equivalence of codes over rings and modules [J].

Dinh, HQ ;

López-Permouth, SR .

FINITE FIELDS AND THEIR APPLICATIONS, 2004, 10 (04) :615-625

[3] On the equivalence of codes over finite rings [J].

Dinh, HQ ;

López-Permouth, SR .

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 2004, 15 (01) :37-50

[4]

Dougherty S. T., 1999, HOKKAIDO MATH J, V28, P253, DOI [10.14492/hokmj/1351001213, DOI 10.14492/H0KMJ/1351001213]

[5] SHADOW CODES AND WEIGHT ENUMERATORS [J].

DOUGHERTY, ST .

IEEE TRANSACTIONS ON INFORMATION THEORY, 1995, 41 (03) :762-768

[6]

DOUGHERTY ST, INT J INFOR IN PRESS

[7] Independence of vectors in codes over rings [J].

Dougherty, Steven T. ;

Liu, Hongwei .

DESIGNS CODES AND CRYPTOGRAPHY, 2009, 51 (01) :55-68

[8] MDS codes over finite principal ideal rings [J].

Dougherty, Steven T. ;

Kim, Jon-Lark ;

Kulosman, Hamid .

DESIGNS CODES AND CRYPTOGRAPHY, 2009, 50 (01) :77-92

[9]

Greferath M, 2006, LECT NOTES PURE APPL, V248, P205

[10] Finite-ring combinatorics and MacWilliams' equivalence theorem [J].

Greferath, M ;

Schmidt, SE .

JOURNAL OF COMBINATORIAL THEORY SERIES A, 2000, 92 (01) :17-28

← 1 2 →