Parameters of LCD BCH codes with two lengths

Haode Yan; Hao Liu; Chengju Li; Shudi Yang

doi:10.3934/amc.2018034

Parameters of LCD BCH codes with two lengths

Haode Yan
, Hao Liu
, Chengju Li^*
, Shudi Yang

^*此作品的通讯作者

软件工程学院

Southwest Jiaotong University
Hong Kong University of Science and Technology
Qufu Normal University

科研成果: 期刊稿件 › 文章 › 同行评审

46 引用（Scopus）

摘要

In this paper, we study LCD BCH codes over the finite field GF(q) with two types of lengths n, where n = q^l + 1 and n = (q^l + 1)/(q + 1). Several classes of LCD BCH codes are given and their parameters are determined or bounded by exploring the cyclotomic cosets modulo n. For n = q^l + 1, we determine the dimensions of the codes with designed distance δ, where (Equation presented). For n = (q^l + 1)/(q + 1), the dimensions of the codes with designed distance δ are presented, where (Equation presented).

源语言	英语
页（从-至）	579-594
页数	16
期刊	Advances in Mathematics of Communications
卷	12
期	3
DOI	https://doi.org/10.3934/amc.2018034
出版状态	已出版 - 2018

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title = "Parameters of LCD BCH codes with two lengths",

abstract = "In this paper, we study LCD BCH codes over the finite field GF(q) with two types of lengths n, where n = ql + 1 and n = (ql + 1)/(q + 1). Several classes of LCD BCH codes are given and their parameters are determined or bounded by exploring the cyclotomic cosets modulo n. For n = ql + 1, we determine the dimensions of the codes with designed distance δ, where (Equation presented). For n = (ql + 1)/(q + 1), the dimensions of the codes with designed distance δ are presented, where (Equation presented).",

keywords = "BCH codes, Cyclic codes, LCD codes, Linear codes, Reversible codes",

author = "Haode Yan and Hao Liu and Chengju Li and Shudi Yang",

note = "Publisher Copyright: {\textcopyright} 2018 AIMS.",

year = "2018",

doi = "10.3934/amc.2018034",

language = "英语",

volume = "12",

pages = "579--594",

journal = "Advances in Mathematics of Communications",

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TY - JOUR

T1 - Parameters of LCD BCH codes with two lengths

AU - Yan, Haode

AU - Liu, Hao

AU - Li, Chengju

AU - Yang, Shudi

PY - 2018

Y1 - 2018

N2 - In this paper, we study LCD BCH codes over the finite field GF(q) with two types of lengths n, where n = ql + 1 and n = (ql + 1)/(q + 1). Several classes of LCD BCH codes are given and their parameters are determined or bounded by exploring the cyclotomic cosets modulo n. For n = ql + 1, we determine the dimensions of the codes with designed distance δ, where (Equation presented). For n = (ql + 1)/(q + 1), the dimensions of the codes with designed distance δ are presented, where (Equation presented).

AB - In this paper, we study LCD BCH codes over the finite field GF(q) with two types of lengths n, where n = ql + 1 and n = (ql + 1)/(q + 1). Several classes of LCD BCH codes are given and their parameters are determined or bounded by exploring the cyclotomic cosets modulo n. For n = ql + 1, we determine the dimensions of the codes with designed distance δ, where (Equation presented). For n = (ql + 1)/(q + 1), the dimensions of the codes with designed distance δ are presented, where (Equation presented).

KW - BCH codes

KW - Cyclic codes

KW - LCD codes

KW - Linear codes

KW - Reversible codes

UR - https://www.scopus.com/pages/publications/85052094418

U2 - 10.3934/amc.2018034

DO - 10.3934/amc.2018034

M3 - 文章

AN - SCOPUS:85052094418

SN - 1930-5346

VL - 12

SP - 579

EP - 594

JO - Advances in Mathematics of Communications

JF - Advances in Mathematics of Communications

IS - 3

ER -

Parameters of LCD BCH codes with two lengths

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