Complete weight enumerators of some linear codes from quadratic forms

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• 作者：Dan Zhang ; Cuiling Fan ; Daiyuan Peng ; Xiaohu Tang
• 关键词：Linear codes ; Codes with few weights ; Quadratic form ; Weight distribution ; Complete weight enumerator
• 刊名：Cryptography and Communications
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：9
• 期：1
• 页码：151-163
• 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

Linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, a construction of q-ary linear codes with few weights employing general quadratic forms over the finite field \({\mathbb {F}}_{q}\) is proposed, where q is an odd prime power. This generalizes some earlier constructions of p-ary linear codes from quadratic bent functions over the prime field \({\mathbb {F}}_{p}\), where p is an odd prime. The complete weight enumerators of the resultant q-ary linear codes are also determined.