Linear codes from simplicial complexes over F2n

被引：0

作者：

Liu, Hongwei ^{[1
]}

Yu, Zihao ^{[1
]}

机构：

[1] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China

来源：

DESIGNS CODES AND CRYPTOGRAPHY | 2024年 / 92卷 / 10期

基金：

中国国家自然科学基金;

关键词：

Linear code; Subfield code; Simplicial complex; Griesmer code;

D O I：

10.1007/s10623-024-01424-8

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this article we mainly study linear codes over F(2)n and their binary subfield codes. We construct linear codes over F(2)n whose defining sets are the certain subsets of F(2)(m)n obtained from mathematical objects called simplicial complexes. We use a result in LFSR sequences to illustrate the relation of the weights of codewords in two special codes obtained from simplical complexes and then determin the parameters of these codes. We construct fiveinfinite families of distance optimal codes and give sufficient conditions for these codes to be minimal.

引用

页码：2993 / 3016

页数：24

共 16 条

[1] Minimal vectors in linear codes [J].

Ashikhmin, A ;

Barg, A .

IEEE TRANSACTIONS ON INFORMATION THEORY, 1998, 44 (05) :2010-2017

[2]

Bonisoli A., 1984, ARS COMBINATORIA, V18, P181

[3] Linear codes from simplicial complexes [J].

Chang, Seunghwan ;

Hyun, Jong Yoon .

DESIGNS CODES AND CRYPTOGRAPHY, 2018, 86 (10) :2167-2181

[4] The Subfield Codes of Ovoid Codes [J].

Ding, Cunsheng ;

Heng, Ziling .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2019, 65 (08) :4715-4729

[5]

Golomb SW., 2005, SIGNAL DESIGN GOOD C, DOI 10.1017/CBO9780511546907

[6]

Grassl M., Bounds on the minimum distance of linear codes and quantum codes

[7] A BOUND FOR ERROR-CORRECTING CODES [J].

GRIESMER, JH .

IBM JOURNAL OF RESEARCH AND DEVELOPMENT, 1960, 4 (05) :532-542

[8] New Constructions of Optimal Linear Codes From Simplicial Complexes [J].

Hu, Zhao ;

Xu, Yunge ;

Li, Nian ;

Zeng, Xiangyong ;

Wang, Lisha ;

Tang, Xiaohu .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2024, 70 (03) :1823-1835

[9]

Huffman WC., 2010, FUNDAMENTALS ERROR C

[10] Infinite Families of Optimal Linear Codes Constructed From Simplicial Complexes [J].

Hyun, Jong Yoon ;

Lee, Jungyun ;

Lee, Yoonjin .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2020, 66 (11) :6762-6773

← 1 2 →