Hasse–Weil bound for additive cyclic codes

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• 作者：Cem Güneri ; Ferruh Özbudak ; Funda Özdemir
• 关键词：Additive cyclic code ; Algebraic curve over a finite field ; Hasse–Weil bound ; BCH bound
• 刊名：Designs, Codes and Cryptography
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：82
• 期：1-2
• 页码：249-263
• 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

We obtain a bound on the minimum distance of additive cyclic codes via the number of rational points on certain algebraic curves over finite fields. This is an extension of the analogous bound in the case of classical cyclic codes. Our result is the only general bound on such codes aside from Bierbrauer’s BCH bound. We compare our bounds’ performance against the BCH bound for additive cyclic codes in a special case and provide examples where it yields better results.