NNMDS codes
type: Item
instance of: scholarly article
title: NNMDS codes
zbMATH Open document ID: 1266.94032
author: Hongxi Tong
published in: Journal of Systems Science and Complexity
publication date: 2013-02-06T00:00:00Z
review text: A linear \([n,k,d]_q\) code is a subspace of dimension \(k\) in \(F_q^n\) with minimum Hamming distance \(q\). The Singleton bound gives that \(d \leq n-k+1.\) The Singleton defect is defined as \(s(C) = n+1-k-d.\) A code meeting the Singleton bound is known as a maximum distance separable (MDS) code. Codes with \(s(C)=s(C^\perp)=1\) are known as near maximum distance separable (NMDS) codes. The author extends this definition to study codes with \(s(C)=s(C^\perp)=2\), which the author calls NNMDS codes. The author gives an upper bound on the length of such codes and gives several necessary and sufficient conditions for their existence.
reviewed by: Steven T. Dougherty
Mathematics Subject Classification ID: 94B05
zbMATH DE Number: 6134670
zbMATH Keywords: generalized Hamming weights
zbMATH Keywords: linear codes
zbMATH Keywords: MDS codes
zbMATH Keywords: near-MDS codes
zbMATH Keywords: Singleton defects
MaRDI profile type: Publication
full work available at URL: s11424-012-0041-5
OpenAlex ID: W3188899691
cites work: Q4146667
cites work: Almost MDS codes
cites work: Q4242008
cites work: On near-MDS codes
cites work: Algebraic function fields and codes
cites work: Near-MDS codes over some small fields
cites work: NMDS codes of maximal length over F/sub q/,8≤q≤11
cites work: Generalized Hamming weights for linear codes
DOI: 10.1007/S11424-012-0041-5
description: scientific article; zbMATH DE number 6134670