Remarks on low weight codewords of generalized affine and projective Reed-Muller codes
Information Theory
2013-04-09 v4 math.IT
Abstract
We propose new results on low weight codewords of affine and projective generalized Reed-Muller codes. In the affine case we prove that if the size of the working finite field is large compared to the degree of the code, the low weight codewords are products of affine functions. Then in the general case we study some types of codewords and prove that they cannot be second, thirds or fourth weight depending on the hypothesis. In the projective case the second distance of generalized Reed-Muller codes is estimated, namely a lower bound and an upper bound of this weight are given.
Keywords
Cite
@article{arxiv.1203.4592,
title = {Remarks on low weight codewords of generalized affine and projective Reed-Muller codes},
author = {Stéphane Ballet and Robert Rolland},
journal= {arXiv preprint arXiv:1203.4592},
year = {2013}
}
Comments
New version taking into account recent results from Elodie Leducq on the characterization of the next-to-minimal codewords (cf. arXiv:1203.5244)