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

作     者：Zeng, Xiangyong Shan, Jinyong Hu, Lei 

作者机构：Hubei Univ Fac Math & Comp Sci Wuhan 430062 Peoples R China Chinese Acad Sci State Key Lab Informat Secur Grad Sch Beijing 100049 Peoples R China 

出 版 物：《FINITE FIELDS AND THEIR APPLICATIONS》 (有限域及其应用)

年 卷 期：2012年第18卷第1期

页      面：70-92页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：National Natural Science Foundation of China (NSFC) NSFC [61070172, 10990011] National Basic Research Program of China [2007CB311201] 

主　　题：Cyclic code BCH code Triple-error-correcting code Minimum distance Almost perfect nonlinear function 

摘      要：Based on a sufficient condition proposed by Hollmann and Xiang for constructing triple-error-correcting codes, the minimum distance of a binary cyclic code C-1,C-3,C-13 with three zeros alpha, alpha(3), and alpha(13) of length 2(m) - 1 and the weight divisibility of its dual code are studied, where m = 5 is odd and a is a primitive element of the finite field F-2m. The code C-1,C-3,C-13 is proven to have the same weight distribution as the binary triple-error-correcting primitive BCH code C-1,C-3,C-5 of the same length. (C) 2011 Elsevier Inc. All rights reserved.