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
收藏
页码：27 / 45
页数：19
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