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

C\'icero Carvalho; Victor G.L. Neumann

arxiv: 1701.01663 · v1 · pith:YWBAGDMRnew · submitted 2017-01-06 · 💻 cs.IT · math.AG· math.IT

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

C\'icero Carvalho , Victor G.L. Neumann This is my paper

classification 💻 cs.IT math.AGmath.IT

keywords next-to-minimalcodesprojectivereed-mullervaluesweightweightsarrangement

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

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