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On the covering radius of first order generalized Reed-Muller codes
Published 10 Feb 2011 in math.NT, cs.IT, and math.IT | (1102.2122v1)
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.
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