On the minimum length of quaternary linear codes of dimension five
type: Item
instance of: scholarly article
title: On the minimum length of quaternary linear codes of dimension five
zbMATH Open document ID: 0934.94018
DOI: 10.1016/S0012-365X(98)00354-9
author: I. Landjev
author: Tatsuya Maruta
published in: Discrete Mathematics
publication date: 2000-02-12T00:00:00Z
review text: Let \(n_q(k,d)\) denote the smallest length of a linear code of length \(n\), dimension \(k\) and minimum distance \(d\). This paper proves the nonexistence of quaternary codes with parameters \([n,k,d]\) being one of \([190,5,141]\), \([239,5,178]\), \([275,5,205]\), \([288,5,215]\), \([291,5,217]\), or \([488,5,365]\). This leads to improved lower bounds for \(n_4(5,d)\) for \(d=141, 142\) and determines the precise value of \(n_4(5,d)\) for \(d=178, 205, 206, 215, 217, 218, 365, 366, 367, 368\). The paper also presents an updated table of \(n_4(5,d)\).
reviewed by: Tor Helleseth
Mathematics Subject Classification ID: 94B05
zbMATH DE Number: 1334523
zbMATH Keywords: optimal codes
zbMATH Keywords: minihypers
zbMATH Keywords: nonexistence of quaternary codes
zbMATH Keywords: lower bounds
MaRDI profile type: Publication
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full work available at URL: s0012-365x(98)00354-9
OpenAlex ID: W2768501565
description: scientific article; zbMATH DE number 1334523