On the second Hamming weight of some Reed-Muller type codes
Information Theory
2013-08-27 v2 Commutative Algebra
math.IT
Abstract
We study affine cartesian codes, which are a Reed-Muller type of evaluation codes, where polynomials are evaluated at the cartesian product of n subsets of a finite field F_q. These codes appeared recently in a work by H. Lopez, C. Renteria-Marquez and R. Villareal and, in a generalized form, in a work by O. Geil and C. Thomsen. Using methods from Gr\"obner basis theory we determine the second Hamming weight (also called next-to-minimal weight) for particular cases of affine cartesian codes and also some higher Hamming weights of this type of code.
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@article{arxiv.1306.4727,
title = {On the second Hamming weight of some Reed-Muller type codes},
author = {Cicero Carvalho},
journal= {arXiv preprint arXiv:1306.4727},
year = {2013}
}
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