On the minimum length of linear codes over the field of 9 elements
type: Item
instance of: scholarly article
title: On the minimum length of linear codes over the field of 9 elements
zbMATH Open document ID: 1361.94054
author: Kazuki Kumegawa
author: Ysukasa Okazaki
author: Tatsuya Maruta
published in: The Electronic Journal of Combinatorics
publication date: 2017-04-10T00:00:00Z
full work available at URL: v24i1p50
review text: Summary: We construct a lot of new \([n, 4, d]_9\) codes whose lengths are close to the Griesmer bound and prove the nonexistence of some linear codes attaining the Griesmer bound using some geometric techniques through projective geometries to determine the exact value of \(n_9(4,d)\) or to improve the known bound on \(n_9(4,d)\) for given values of \(d\), where \(n_q(k,d)\) is the minimum length \(n\) for which an \([n, k, d]_q\) code exists. We also give the updated table for \(n_9(4,d)\) for all \(d\) except some known cases.
Mathematics Subject Classification ID: 94B05
Mathematics Subject Classification ID: 94B65
zbMATH DE Number: 6703742
zbMATH Keywords: optimal linear codes
zbMATH Keywords: Griesmer bound
zbMATH Keywords: projective dual
zbMATH Keywords: geometric puncturing
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6703742