Paper Info
Title
On the non-minimality of the largest weight codewords in the binary Reed-Muller codes.
Abstract
The study of minimal codewords in linear codes was motivated by Massey who described how minimal codewords of a linear code define access structures for secret sharing schemes. As a consequence of his article, Borissov, Manev, and Nikova initiated the study of minimal codewords in the binary Reed-Muller codes. They counted the number of non-minimal codewords of weight 2d in the binary Reed-Muller codes RM(r, in), and also gave results on the non-minimality of codewords of large weight in the binary Reed-Muller codes RM(r, in). The results of Borissov, Manev, and Nikova regarding the counting of the number of non-minimal codewords of small weight in RM(r,m) were improved by Schillewaert, Storme, and Thas who counted the number of non-minimal codewords of weight smaller than 3d in RM(r,m). This article now presents new results on the non-minimality of large weight codewords in RM(r, m).
Year
DOI
Venue
2011
10.3934/amc.2011.5.333
ADVANCES IN MATHEMATICS OF COMMUNICATIONS
Keywords
DocType
Volume
Reed-Muller codes,minimal codewords
Journal
5
Issue
ISSN
Citations 
SP2
1930-5346
0
PageRank 
References 
Authors
0.34
2
2
Name
Order
Citations
PageRank
Andreas Klein161.90
Leo Storme219738.07