On quasi-twisted codes over finite fields

被引：44

作者：

Jia, Yan ^{[1
]}

机构：

[1] Nanyang Technol Univ, SPMS MAS 0301, Div Math Sci, Singapore 637371, Singapore

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2012年 / 18卷 / 02期

基金：

新加坡国家研究基金会;

关键词：

Quasi-twisted code; Finite field; Generalized discrete Fourier transform; Repeated-root case; Nonrepeated-root case; Construction; ALGEBRAIC STRUCTURE;

D O I：

10.1016/j.ffa.2011.08.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In coding theory, quasi-twisted (QT) codes form an important class of codes which has been extensively studied. We decompose a QT code to a direct sum of component codes linear codes over rings. Furthermore, given the decomposition of a QT code, we can describe the decomposition of its dual code. We also use the generalized discrete Fourier transform to give the inverse formula for both the nonrepeated-root and repeated-root cases. Then we produce a formula which can be used to construct a QT code given the component codes. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：237 / 257

页数：21

共 5 条

[1] The structure of 1-generator quasi-twisted codes and new linear codes [J].

Aydin, N ;

Siap, I ;

Ray-Chaudhuri, DK .

DESIGNS CODES AND CRYPTOGRAPHY, 2001, 24 (03) :313-326

[2] The Magma algebra system .1. The user language [J].

Bosma, W ;

Cannon, J ;

Playoust, C .

JOURNAL OF SYMBOLIC COMPUTATION, 1997, 24 (3-4) :235-265

[3]

Lidl R., 1997, Finite Fields

[4] On the algebraic structure of quasi-cyclic codes IV:: Repeated roots [J].

Ling, S ;

Niederreiter, H ;

Solé, P .

DESIGNS CODES AND CRYPTOGRAPHY, 2006, 38 (03) :337-361

[5] On the algebraic structure of quasi-cyclic codes II:: Chain rings [J].

Ling, S ;

Solé, P .

DESIGNS CODES AND CRYPTOGRAPHY, 2003, 30 (01) :113-130

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