A triple-error-correcting cyclic code from the Gold and Kasami-Welch APN power functions

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• 作者：Xiangyong Zeng^a ; ^{xiangyongzeng@yahoo.com.cn} ; Jinyong Shan^a ; ^{shan20051@126.com} ; Lei Hu^b ; ^hu@is.ac.cn
• 关键词：94B15 ; 94A60
• 刊名：Finite Fields and Their Applications
• 出版年：2012
• 出版时间：January, 2012
• 年：2012
• 卷：18
• 期：1
• 页码：70-92
• 全文大小：292 K

文摘

Based on a sufficient condition proposed by Hollmann and Xiang for constructing triple-error-correcting codes, the minimum distance of a binary cyclic code with three zeros , , and of length and the weight divisibility of its dual code are studied, where is odd and is a primitive element of the finite field . The code is proven to have the same weight distribution as the binary triple-error-correcting primitive BCH code of the same length.