Geometric approach to the MacWilliams Extension Theorem for codes over module alphabets

被引：3

作者：

Dyshko, Serhii ^{[1
]}

机构：

[1] Univ Toulon & Var, IMATH, BP 20132, F-83957 La Garde, France

来源：

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING | 2017年 / 28卷 / 04期

关键词：

MacWilliams Extension Theorem; Hamming isometry; Module alphabet; MDS code; Group code; Matrix module; FINITE RINGS; LINEAR CODES; EQUIVALENCE;

D O I：

10.1007/s00200-017-0324-0

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

The minimal code length for which there exists an unextendable Hamming isometry of a linear code defined over a matrix module alphabet is found. An extension theorem for MDS codes over module alphabets is proved. An extension theorem for the case of MDS group codes is observed.

引用

页码：295 / 309

页数：15

共 50 条

[31] An extension theorem for linear codes
Hill, R
DESIGNS CODES AND CRYPTOGRAPHY, 1999, 17 (1-3) : 151 - 157
[32] An Extension Theorem for Linear Codes
Ray Hill
Designs, Codes and Cryptography, 1999, 17 : 151 - 157
[33] New DNA Codes from Cyclic Codes over Mixed Alphabets
Dinh, Hai Q.
Pathak, Sachin
Upadhyay, Ashish Kumar
Yamaka, Woraphon
MATHEMATICS, 2020, 8 (11) : 1 - 24
[34] MacWilliams identities for linear codes over finite Frobenius rings
Honold, T
Landjev, I
FINITE FIELDS AND APPLICATIONS, 2001, : 276 - 292
[35] A PRODUCT CONSTRUCTION FOR PERFECT CODES OVER ARBITRARY ALPHABETS
PHELPS, KT
IEEE TRANSACTIONS ON INFORMATION THEORY, 1984, 30 (05) : 769 - 771
[36] On perfect codes over non prime power alphabets
Heden, Olof
ERROR-CORRECTING CODES, FINITE GEOMETRIES AND CRYPTOGRAPHY, 2010, 523 : 173 - 184
[37] The extension theorem for Lee and Euclidean weight codes over integer residue rings
Serhii Dyshko
Designs, Codes and Cryptography, 2019, 87 : 1253 - 1269
[38] The extension theorem for Lee and Euclidean weight codes over integer residue rings
Dyshko, Serhii
DESIGNS CODES AND CRYPTOGRAPHY, 2019, 87 (06) : 1253 - 1269
[39] A new extension theorem for linear codes
Maruta, T
FINITE FIELDS AND THEIR APPLICATIONS, 2004, 10 (04) : 674 - 685
[40] A generalized extension theorem for linear codes
Maruta, Tatsuya
Yoshida, Yuri
DESIGNS CODES AND CRYPTOGRAPHY, 2012, 62 (01) : 121 - 130

← 1 2 3 4 5 →