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.
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}
}