The weight distribution of a family of \(p\) -ary cyclic codes
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- 作者：Dabin Zheng (1)
Xiaoqiang Wang (1)
Xiangyong Zeng (1) (2)
Lei Hu (2) (3)
1. Faculty of Mathematics and Statistics ; Hubei University ; Wuhan ; 430062 ; China
2. State Key Laboratory of Information Security ; Institute of Information Engineering ; Chinese Academy of Sciences ; Beijing ; 100093 ; China
3. Beijing Center for Mathematics and Information Interdisciplinary Sciences ; Beijing ; 100048 ; China - 关键词：Cyclic code ; Weight distribution ; Exponential sum ; Quadratic form ; 11T71 ; 94B15
- 刊名：Designs, Codes and Cryptography
- 出版年：2015
- 出版时间：May 2015
- 年：2015
- 卷：75
- 期：2
- 页码：263-275
- 全文大小：216 KB
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- 刊物主题：Mathematics
Combinatorics
Coding and Information Theory
Data Structures, Cryptology and Information Theory
Data Encryption
Discrete Mathematics in Computer Science
Information, Communication and Circuits - 出版者：Springer Netherlands
- ISSN：1573-7586
文摘
Let \(p\) be an odd prime, and \(m\) and \(k\) be two positive integers with \(\frac{m}{\gcd (m,k)}\) being odd. This paper determines the weight distribution of a family of \(p\) -ary cyclic codes over \({\mathbb {F}}_p\) whose duals have three zeros \(\alpha ^{-2}, \alpha ^{-(p^{2k}+1)}\) and \(\alpha ^{-(p^{4k}+1)}\) , where \(\alpha \) is a primitive element of \({\mathbb {F}}_{p^m}\) .