New good quasi-cyclic codes and codes with improved minimum distance

Eric Chen; Fredrik Jönsson

New good quasi-cyclic codes and codes with improved minimum distance

Forskningsoutput: Bidrag till specialistpublikation › Artikel

Sammanfattning

One of the most important and challenging problems in coding theory is to construct codes with optimal parameters. As a generalization of cyclic codes, quasi-cyclic (QC) codes as well as quasi-twisted (QT) codes have been shown to contain record-breaking codes. In this paper, various computer algorithms have been used to search for good QC codes. A lot of good new QC codes have been found and they have been used to construct new linear codes. A total 11 new codes that improve the bound on the minimum distance are presented.

Originalspråk	Engelska
Specialistpublikation	Journal of Algebra Combinatorics Discrete Structures and Applications
Status	Accepterad/under tryckning - 2022-juli-28

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title = "New good quasi-cyclic codes and codes with improved minimum distance",

abstract = "One of the most important and challenging problems in coding theory is to construct codes with optimal parameters. As a generalization of cyclic codes, quasi-cyclic (QC) codes as well as quasi-twisted (QT) codes have been shown to contain record-breaking codes. In this paper, various computer algorithms have been used to search for good QC codes. A lot of good new QC codes have been found and they have been used to construct new linear codes. A total 11 new codes that improve the bound on the minimum distance are presented.",

keywords = "Finite fields, Linear codes, Quasi-cyclic codes, Algorithms",

author = "Eric Chen and Fredrik J{\"o}nsson",

year = "2022",

month = jul,

day = "28",

language = "English",

journal = "Journal of Algebra Combinatorics Discrete Structures and Applications",

issn = "2148-838X",

publisher = "Jacodesmath Institute",

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TY - GEN

T1 - New good quasi-cyclic codes and codes with improved minimum distance

AU - Chen, Eric

AU - Jönsson, Fredrik

PY - 2022/7/28

Y1 - 2022/7/28

N2 - One of the most important and challenging problems in coding theory is to construct codes with optimal parameters. As a generalization of cyclic codes, quasi-cyclic (QC) codes as well as quasi-twisted (QT) codes have been shown to contain record-breaking codes. In this paper, various computer algorithms have been used to search for good QC codes. A lot of good new QC codes have been found and they have been used to construct new linear codes. A total 11 new codes that improve the bound on the minimum distance are presented.

AB - One of the most important and challenging problems in coding theory is to construct codes with optimal parameters. As a generalization of cyclic codes, quasi-cyclic (QC) codes as well as quasi-twisted (QT) codes have been shown to contain record-breaking codes. In this paper, various computer algorithms have been used to search for good QC codes. A lot of good new QC codes have been found and they have been used to construct new linear codes. A total 11 new codes that improve the bound on the minimum distance are presented.

KW - Finite fields

KW - Linear codes

KW - Quasi-cyclic codes

KW - Algorithms

M3 - Article

JO - Journal of Algebra Combinatorics Discrete Structures and Applications

JF - Journal of Algebra Combinatorics Discrete Structures and Applications

SN - 2148-838X

ER -