On the second Hamming weight of some Reed-Muller type codes

被引：27
|
作者：
Carvalho, Cicero [1 ]
机构：
[1] Univ Fed Uberlandia, Fac Matemat, BR-38408902 Uberlandia, MG, Brazil
来源：
FINITE FIELDS AND THEIR APPLICATIONS | 2013年 / 24卷
关键词：
Affine variety codes; Affine cartesian codes; Hamming weights;
D O I：
10.1016/j.ffa.2013.06.004
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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 (see Lopez et al. (2013) [11]) and, in a generalized form, in a work by O. Geil and C. Thomsen (see Geil and Thomsen (2013) 19]). 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. (C) 2013 Elsevier Inc. All rights reserved.
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页码：88 / 94
页数：7
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