On the Covering Radius of First-Order Generalized Reed–Muller Codes

We generalize to any finite Fq fields a theorem about covering radius of codes of strength 2 proved by Helleseth and coworkers. Then,using this result and partial covering radius, we give bounds for the covering radius of first-order generalized Reed-Muller codes. Finally, using Magma, we get some improvements for F3.

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