A symmetric Roos bound for linear codes

Iwan M. Duursma; Ruud Pellikaan

doi:10.1016/j.jcta.2006.03.020

A symmetric Roos bound for linear codes

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

Abstract

The van Lint-Wilson AB-method yields a short proof of the Roos bound for the minimum distance of a cyclic code. We use the AB-method to obtain a different bound for the weights of a linear code. In contrast to the Roos bound, the role of the codes A and B in our bound is symmetric. We use the bound to prove the actual minimum distance for a class of dual BCH codes of length q² - 1 over F_q. We give cyclic codes [63, 38, 16] and [65, 40, 16] over F₈ that are better than the known [63, 38, 15] and [65, 40, 15] codes.

Original language	English (US)
Pages (from-to)	1677-1688
Number of pages	12
Journal	Journal of Combinatorial Theory. Series A
Volume	113
Issue number	8
DOIs	https://doi.org/10.1016/j.jcta.2006.03.020
State	Published - Nov 2006

Keywords

Cyclic code
Dual BCH code
Minimum distance bound
Roos bound

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

Online availability

10.1016/j.jcta.2006.03.020

Library availability

Discover UIUC Full Text

Cite this

@article{566fe6b688bb4feabbcabe95cb0fcf0f,

title = "A symmetric Roos bound for linear codes",

abstract = "The van Lint-Wilson AB-method yields a short proof of the Roos bound for the minimum distance of a cyclic code. We use the AB-method to obtain a different bound for the weights of a linear code. In contrast to the Roos bound, the role of the codes A and B in our bound is symmetric. We use the bound to prove the actual minimum distance for a class of dual BCH codes of length q2 - 1 over Fq. We give cyclic codes [63, 38, 16] and [65, 40, 16] over F8 that are better than the known [63, 38, 15] and [65, 40, 15] codes.",

keywords = "Cyclic code, Dual BCH code, Minimum distance bound, Roos bound",

author = "Duursma, {Iwan M.} and Ruud Pellikaan",

year = "2006",

month = nov,

doi = "10.1016/j.jcta.2006.03.020",

language = "English (US)",

volume = "113",

pages = "1677--1688",

journal = "Journal of Combinatorial Theory. Series A",

issn = "0097-3165",

publisher = "Academic Press Inc.",

number = "8",

}

TY - JOUR

T1 - A symmetric Roos bound for linear codes

AU - Duursma, Iwan M.

AU - Pellikaan, Ruud

PY - 2006/11

Y1 - 2006/11

N2 - The van Lint-Wilson AB-method yields a short proof of the Roos bound for the minimum distance of a cyclic code. We use the AB-method to obtain a different bound for the weights of a linear code. In contrast to the Roos bound, the role of the codes A and B in our bound is symmetric. We use the bound to prove the actual minimum distance for a class of dual BCH codes of length q2 - 1 over Fq. We give cyclic codes [63, 38, 16] and [65, 40, 16] over F8 that are better than the known [63, 38, 15] and [65, 40, 15] codes.

AB - The van Lint-Wilson AB-method yields a short proof of the Roos bound for the minimum distance of a cyclic code. We use the AB-method to obtain a different bound for the weights of a linear code. In contrast to the Roos bound, the role of the codes A and B in our bound is symmetric. We use the bound to prove the actual minimum distance for a class of dual BCH codes of length q2 - 1 over Fq. We give cyclic codes [63, 38, 16] and [65, 40, 16] over F8 that are better than the known [63, 38, 15] and [65, 40, 15] codes.

KW - Cyclic code

KW - Dual BCH code

KW - Minimum distance bound

KW - Roos bound

UR - http://www.scopus.com/inward/record.url?scp=33748420796&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33748420796&partnerID=8YFLogxK

U2 - 10.1016/j.jcta.2006.03.020

DO - 10.1016/j.jcta.2006.03.020

M3 - Article

AN - SCOPUS:33748420796

SN - 0097-3165

VL - 113

SP - 1677

EP - 1688

JO - Journal of Combinatorial Theory. Series A

JF - Journal of Combinatorial Theory. Series A

IS - 8

ER -

A symmetric Roos bound for linear codes

Abstract

Keywords

ASJC Scopus subject areas

Online availability

Library availability

Related links

Fingerprint

Cite this