Complete weight enumerators of a family of three-weight linear codes

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• 作者：Shudi Yang ; Zheng-An Yao
• 关键词：Linear code ; Complete weight enumerator ; Gaussian period ; Gauss sum
• 刊名：Designs, Codes and Cryptography
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：82
• 期：3
• 页码：663-674
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Combinatorics; Coding and Information Theory; Data Structures, Cryptology and Information Theory; Data Encryption; Discrete Mathematics in Computer Science; Information and Communication, Circuits;
• 出版者：Springer US
• ISSN：1573-7586
• 卷排序：82

文摘

Linear codes have been an interesting topic in both theory and practice for many years. In this paper, for an odd prime p, we present the explicit complete weight enumerator of a family of p-ary linear codes constructed with defining set. The weight enumerator is an immediate result of the complete weight enumerator, which shows that the codes proposed in this paper are three-weight linear codes. Additionally, all nonzero codewords are minimal and thus they are suitable for secret sharing.