English

On the covering radius of first order generalized Reed-Muller codes

Number Theory 2011-02-11 v1 Information Theory math.IT

Abstract

We generalize to any q a theorem about covering radius of linear codes proved by Helleseth, Klove and Mykkelvit. Then we determine the covering radius of first order generalized Reed-Muller codes in second order generalized Reed-Muller codes. Using these results, we are able to give bounds for the covering radius of first order generalized Reed-Muller codes. Finaly, using Magma, we get some improvements for q=3.

Keywords

Cite

@article{arxiv.1102.2122,
  title  = {On the covering radius of first order generalized Reed-Muller codes},
  author = {Elodie Leducq},
  journal= {arXiv preprint arXiv:1102.2122},
  year   = {2011}
}