A gap in GRM code weight distributions
type: Item
instance of: scholarly article
title: A gap in GRM code weight distributions
zbMATH Open document ID: 1003.94028
DOI: 10.1023/A:1008307729806
author: Todd D. Vance
published in: Designs, Codes and Cryptography
publication date: 2003-01-08T00:00:00Z
review text: The weight distribution of generalized Reed-Muller (GRM) codes is open, except for some particular parameters. This paper contributes to the research on this problem by proving results on weights that cannot occur in GRM codes. Every \([n,k,d]\) GRM code has words of weight 0, \(d\), and \(n\), and obviously no words of weight between 0 and \(d\). Let \(\Delta\) be the largest integer dividing all weights occurring in a code. Then there are no words having weight between \(d + i\Delta\) and \(d+(i+1)\Delta\), \(i \geq 0\). This paper shows that, for some GRM codes, the gap is actually larger: there are no words having weight between \(d\) and \(d+2\Delta\).
Mathematics Subject Classification ID: 94B05
zbMATH DE Number: 1420169
zbMATH Keywords: generalized Reed-Muller code
zbMATH Keywords: weight distribution
reviewed by: Patric R. J. Östergård
MaRDI profile type: Publication
full work available at URL: a:1008307729806
OpenAlex ID: W1484627920
description: scientific article; zbMATH DE number 1420169