The second weight of generalized Reed-Muller codes in most cases

Robert Rolland

The second weight of generalized Reed-Muller codes in most cases

Information Theory 2009-06-30 v2 math.IT

Authors: Robert Rolland

Abstract

The second weight of the Generalized Reed-Muller code of order $d$ over the finite field with $q$ elements is now known for $d <q$ and $d>(n-1)(q-1)$ . In this paper, we determine the second weight for the other values of $d$ which are not multiple of $q-1$ plus 1. For the special case $d=a(q-1)+1$ we give an estimate.

Keywords

generalized Reed-Muller code second weight finite field coding theory weight distribution

Cite

@article{arxiv.0902.0058,
  title  = {The second weight of generalized Reed-Muller codes in most cases},
  author = {Robert Rolland},
  journal= {arXiv preprint arXiv:0902.0058},
  year   = {2009}
}

Comments

This version corrects minor misprints and gives a more detailed proof of a combinatorial lemma

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