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

Software Engineering Institute

Research output: Contribution to journal › Article › peer-review

41 Scopus citations

Abstract

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).

Original language	English
Pages (from-to)	579-594
Number of pages	16
Journal	Advances in Mathematics of Communications
Volume	12
Issue number	3
DOIs	https://doi.org/10.3934/amc.2018034
State	Published - 2018

Keywords

BCH codes
Cyclic codes
LCD codes
Linear codes
Reversible codes

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10.3934/amc.2018034

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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",

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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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