Repeated root cyclic Fq-linear codes over Fql

被引：24

作者：

Cao, Yonglin ^{[1
]}

Gao, Yun ^{[1
]}

机构：

[1] Shandong Univ Technol, Sch Sci, Zibo 255091, Shandong, Peoples R China

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2015年 / 31卷

基金：

中国国家自然科学基金;

关键词：

Repeated root cyclic F-q-linear code; Finite chain ring; Linear code over finite chain ring; Dual code; DUAL ADDITIVE CODES; CLASSIFICATION;

D O I：

10.1016/j.ffa.2014.10.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let F-q be a finite field of cardinality q, where q is a power of a prime number p, n a positive multiple of p, l a prime number and F-ql an extension field of F-q with degree l. First, the structure and a canonical form decomposition of any cyclic F-q-linear code over F-ql of length n are presented. Then from this decomposition and by the theory of linear codes over finite chain rings, enumeration, construction and encoder of these codes are investigated. Furthermore, the dual code of any cyclic F-q-linear code over F-ql of length n is studied. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：202 / 227

页数：26

共 16 条

[1]

Bierbrauer J, 2000, J COMB DES, V8, P174, DOI 10.1002/(SICI)1520-6610(2000)8:3<174::AID-JCD3>3.0.CO

[2]

2-T

[3]

Bierbrauer J, 2007, LECT NOTES COMPUT SC, V4547, P276

[4] Quantum error correction via codes over GF (4) [J].

Calderbank, AR ;

Rains, EM ;

Shor, PW ;

Sloane, NJA .

IEEE TRANSACTIONS ON INFORMATION THEORY, 1998, 44 (04) :1369-1387

[5] On the Classification of Hermitian Self-Dual Additive Codes Over GF(9) [J].

Danielsen, Lars Eirik .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2012, 58 (08) :5500-5511

[6] GRAPH-BASED CLASSIFICATION OF SELF-DUAL ADDITIVE CODES OVER FINITE FIELDS [J].

Danielsen, Lars Eirik .

ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 2009, 3 (04) :329-348

[7]

Dey BK, 2005, DESIGN CODE CRYPTOGR, V34, P89, DOI 10.1007/s10623-003-4196-x

[8]

HONOLD T, 2000, ELECT J COMB, V7

[9] On the groups of units of finite commutative chain rings [J].

Hou, XD ;

Leung, KH ;

Ma, SL .

FINITE FIELDS AND THEIR APPLICATIONS, 2003, 9 (01) :20-38

[10]

Huffman W. Cary, 2010, International Journal of Information and Coding Theory, V1, P249, DOI 10.1504/IJICOT.2010.032543

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