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arXiv · 1701.01663

On the next-to-minimal weight of projective Reed-Muller codes

Cícero Carvalho·Victor G. L. Neumann
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Abstract

In this paper we present several values for the next-to-minimal weights of projective Reed-Muller codes. We work over $\mathbb{F}_q$ with $q \geq 3$ since in IEEE-IT 62(11) p. 6300-6303 (2016) we have determined the complete values for the next-to-minimal weights of binary projective Reed-Muller codes. As in loc. cit. here we also find examples of codewords with next-to-minimal weight whose set of zeros is not in a hyperplane arrangement.

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Cícero Carvalho, Victor G. L. Neumann. 2017-01-06. On the next-to-minimal weight of projective Reed-Muller codes. https://arxiv.org/abs/1701.01663

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