A kind of three-weight linear codes

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• 作者：Qiuyan Wang ; Kelan Ding ; Dongdai Lin ; Rui Xue
• 关键词：Authentication codes ; Linear codes ; Secret sharing schemes ; Weight distribution
• 刊名：Cryptography and Communications
• 出版年：2017
• 出版时间：May 2017
• 年：2017
• 卷：9
• 期：3
• 页码：315-322
• 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 with few weights have been constructed through defining sets. Results show that some optimal codes can be obtained if the defining sets were well chosen. In this paper, we investigate the linear codes constructed from the absolute trace function. It is shown that the constructed codes are binary linear codes with three weights. The dual codes of the proposed linear codes are also studied and proved to be optimal or almost optimal.