A class of three-weight linear codes and their complete weight enumerators

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• 作者：Shudi Yang ; Zheng-An Yao ; Chang-An Zhao
• 关键词：Linear code ; Complete weight enumerator ; Weight enumerator ; Gauss sum ; Gauss period
• 刊名：Cryptography and Communications
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：9
• 期：1
• 页码：133-149
• 全文大小：
• 刊物类别：Computer Science
• 刊物主题：Data Structures, Cryptology and Information Theory; Coding and Information Theory; Communications Engineering, Networks; Information and Communication, Circuits; Mathematics of Computing;
• 出版者：Springer US
• ISSN：1936-2455
• 卷排序：9

文摘

Recently, linear codes constructed from defining sets have been investigated extensively and they have many applications. In this paper, for an odd prime p, we propose a class of p-ary linear codes by choosing a proper defining set. Their weight enumerators and complete weight enumerators are presented explicitly. Our results show that they are linear codes with three weights and suitable for the constructions of authentication codes and secret sharing schemes.