On optimal codes over the field with five elements
type: Item
instance of: scholarly article
title: On optimal codes over the field with five elements
zbMATH Open document ID: 1030.94044
DOI: 10.1023/A:1024108609872
author: D. Massart
published in: Designs, Codes and Cryptography
publication date: 2003-08-21T00:00:00Z
review text: Let \(n_q(k,d)\) denote the minimal length of a linear code of dimension \(k\) and minimum distance \(d\) over the field \(\text{GF}(q)\). An important problem in coding theory is to find the exact value of \(n_q(k,d)\), for given \(k\), \(d\) and \(q\). It is known that a full length linear code is equivalent to an arc in a finite projective space. The authors use this equivalence to prove the nonexistence of Griesmer codes over \(\text{GF}(5)\) for \(k=4\) and \(d=33,83,163,164\).
Mathematics Subject Classification ID: 94B27
Mathematics Subject Classification ID: 51E22
Mathematics Subject Classification ID: 94B05
Mathematics Subject Classification ID: 51E21
zbMATH DE Number: 1968865
zbMATH Keywords: Griesmer code
zbMATH Keywords: arc
zbMATH Keywords: linear code
reviewed by: Antonio Cossidente
MaRDI profile type: Publication
full work available at URL: a:1024108609872
OpenAlex ID: W1582685047
description: scientific article; zbMATH DE number 1968865