On the small-weight codewords of some Hermitian codes

被引：9

作者：

Marcolla, Chiara ^{[1
]}

Pellegrini, Marco ^{[2
]}

Sala, Massimiliano ^{[1
]}

机构：

[1] Univ Trento, Dept Math, Trento, Italy

[2] Univ Florence, Dept Math, I-50121 Florence, Italy

来源：

JOURNAL OF SYMBOLIC COMPUTATION | 2016年 / 73卷

关键词：

Affine-variety code; Hamming weight; Hermitian code; Hermitian curve; Linear code; Minimum-weight words;

D O I：

10.1016/j.jsc.2015.03.003

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

For any affine-variety code we show how to construct an ideal whose solutions correspond to codewords with any assigned weight. We are able to obtain geometric characterizations for small-weight codewords for some families of Hermitian codes over any Fe. From these geometric characterizations, we obtain explicit formulas. In particular, we determine the number of minimum-weight codewords for all Hermitian codes with d <= q and all second-weight codewords for distance-3,4 codes. (C) 2015 Elsevier Ltd. All rights reserved.

引用

页码：27 / 45

页数：19

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