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

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

2011-02-10

arxiv.org/abs/1102.2122v1

Mathematics

Number Theory

Scientific paper

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.

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