Covering radius of the Reed-Muller code \(R(1,7)\) -- a simpler proof
type: Item
instance of: scholarly article
title: Covering radius of the Reed-Muller code \(R(1,7)\) -- a simpler proof
zbMATH Open document ID: 0849.94027
published in: Journal of Combinatorial Theory. Series A
publication date: 1996-07-09T00:00:00Z
review text: \textit{J. J. Mykkeltveit} [IEEE Trans. Inf. Theory 26, 359-362 (1980; Zbl 0431.94036)] proved that the covering radius of the Reed-Muller code \(R(1,7)\) equals 56. Mykkeltveit showed this by establishing the nonexistence of a \([57, 8, 25]\) self-complementary code of strength 2. In this paper the author gives a simpler proof which avoids this approach entirely.
Mathematics Subject Classification ID: 94B75
Mathematics Subject Classification ID: 94B65
zbMATH DE Number: 883819
zbMATH Keywords: covering radius
zbMATH Keywords: Reed-Muller code \(R(1,7)\)
author: Xiang-Dong Hou
MaRDI profile type: Publication
full work available at URL: jcta.1996.0055
OpenAlex ID: W1996191578
DOI: 10.1006/JCTA.1996.0055
description: scientific article; zbMATH DE number 883819