A class of perfect ternary constant-weight codes
type: Item
instance of: scholarly article
title: A class of perfect ternary constant-weight codes
zbMATH Open document ID: 0963.94037
DOI: 10.1023/A:1008361925021
author: Mattias Svanström
published in: Designs, Codes and Cryptography
publication date: 2001-01-01T00:00:00Z
review text: A class of perfect ternary constant-weight codes of length \(2^r\), weight \(2^r-1\) and minimum distance 3 is presented. The construction is based on binary Hamming codes. The number of codewords is \(2^{2^r}-1\). For \(r=2\), the construction results in the subcode of the \([4,2,3]\) tetracode consisting of its nonzero codewords. These are the only perfect \(q\)-ary constant-weight codes known to date. These codes can be shortened twice to give two more classes of optimal codes.
Mathematics Subject Classification ID: 94B05
Mathematics Subject Classification ID: 94B65
zbMATH DE Number: 1548350
zbMATH Keywords: constant-weight codes
zbMATH Keywords: ternary codes
zbMATH Keywords: perfect codes
reviewed by: T. Aaron Gulliver
MaRDI profile type: Publication
full work available at URL: a:1008361925021
OpenAlex ID: W1539721799
description: scientific article; zbMATH DE number 1548350