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

Cícero Carvalho; Victor G. L. Neumann

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

Information Theory 2017-03-20 v1 Algebraic Geometry math.IT

Authors: Cícero Carvalho , Victor G. L. Neumann

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.

Keywords

projective Reed-Muller codes next-to-minimal weight codewords hyperplane arrangement finite fields coding theory

Cite

@article{arxiv.1701.01663,
  title  = {On the next-to-minimal weight of projective Reed-Muller codes},
  author = {Cícero Carvalho and Victor G. L. Neumann},
  journal= {arXiv preprint arXiv:1701.01663},
  year   = {2017}
}

Comments

9 pages. arXiv admin note: text overlap with arXiv:1701.01658

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

Abstract

Keywords

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