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

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.