Weight enumerator of some irreducible cyclic codes

被引:0
作者
Fabio Enrique Brochero Martínez
Carmen Rosa Giraldo Vergara
机构
[1] Universidade Federal de Minas Gerais,Departamento de Matemática
来源
Designs, Codes and Cryptography | 2016年 / 78卷
关键词
Cyclic codes; Weight enumerator; Minimum distance; 12E05; 94B05;
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摘要
In this article, we show explicitly all possible weight enumerators for every irreducible cyclic code of length n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end{document} over a finite field Fq\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {F}}_q$$\end{document}, in the case which each prime divisor of n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end{document} is also a divisor of q-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q-1$$\end{document}.
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页码:703 / 712
页数:9
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