Complete weight distributions of two classes of cyclic codes

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• 作者：Ziling Heng ; Qin Yue
• 关键词：Cyclic code ; Complete weight distribution ; Weight distribution ; Quadratic form
• 刊名：Cryptography and Communications
• 出版年：2017
• 出版时间：May 2017
• 年：2017
• 卷：9
• 期：3
• 页码：323-343
• 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

Complete weight distribution can be used to study authentication codes and the Walsh transform of monomial functions over finite fields. Also, the Hamming weight distribution of a code can be obtained from its complete weight distribution. In this paper, we investigate the complete weight distributions of two classes of cyclic codes. We explicitly present the complete weight enumerators of the cyclic codes. Particularly, we partly solve an open problem proposed in Luo and Feng (IEEE Trans. Inf. Theory 54(12), 5345–5353 (2008)).