Extremal self-dual \([40,20,8]\) codes with covering radius 7
type: Item
instance of: scholarly article
title: Extremal self-dual \([40,20,8]\) codes with covering radius 7
zbMATH Open document ID: 1064.94016
author: Masaaki Harada
author: Akihiro Munemasa
author: Kenichiro Tanabe
published in: Finite Fields and their Applications
publication date: 2004-08-06T00:00:00Z
review text: \textit{E. Assmus} and \textit{V. Pless} [IEEE Trans. Inf. Theory 29, 359--363 (1983; Zbl 0504.94028)] showed that the minimum possible covering radius of an extremal doubly-even binary \([40,20,8]\) code is 6, 7, or 8; \textit{M. Harada} and \textit{M. Ozeki} [Discrete Math. 215, 271--281 (2000; Zbl 0974.94027)] found such a code with covering radius 7. Nonexistence of codes with covering radius 6 has been mentioned in the literature, but these results were withdrawn by \textit{M. Ozeki} [IEEE Trans. Inf. Theory 48, 547--556 (2002; Zbl 1064.94020 In the current paper an extremal doubly-even binary \([40,20,8]\) code with covering radius 7 is presented which is not equivalent to the code presented by Harada and Ozeki (loc. cit.). Singly-even codes with these parameters are also discussed, as well as some related 1-designs.
Mathematics Subject Classification ID: 94B05
Mathematics Subject Classification ID: 94B75
zbMATH DE Number: 2083584
zbMATH Keywords: covering radius
zbMATH Keywords: extremal code
zbMATH Keywords: harmonic weight enumerator
zbMATH Keywords: self-dual code
reviewed by: Patric R. J. Östergård
MaRDI profile type: Publication
full work available at URL: j.ffa.2003.08.001
OpenAlex ID: W2004225323
cites work: On the coveting radius of extremal self-dual codes
cites work: On harmonic weight enumerators of binary codes
cites work: Covering radius---Survey and recent results
cites work: A new upper bound on the minimal distance of self-dual codes
cites work: Four fundamental parameters of a code and their combinatorial significance
cites work: Hahn Polynomials, Discrete Harmonics, andt-Designs
cites work: Uniqueness of some linear subcodes of the extended binary Golay code
cites work: Classification of extremal double-circulant self-dual codes of length up to \(62\)
cites work: Extremal self-dual codes with the smallest covering radius
cites work: The mass of extremal doubly-even self-dual codes of length 40
cites work: An upper bound for self-dual codes
cites work: Q4146667
cites work: On the Classification of Self-dual -Codes
cites work: On covering radii and coset weight distributions of extremal binary self-dual codes of length 40
cites work: Jacobi polynomials for singly even self-dual codes and the covering radius problems
cites work: Shadow bounds for self-dual codes
DOI: 10.1016/J.FFA.2003.08.001
description: scientific article; zbMATH DE number 2083584