A Triple-Error-Correcting Cyclic Code from the Gold and Kasami-Welch APN Power Functions

2010/03/31 by Xiangyong Zeng, Zeng, Xiangyong, Jinyong Shan +3
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Cryptographic Implementations and Security #cs.DM #cs.IT #graph theory and CDMA systems #math.IT #msc:94B

paper · pdf · doi:10.48550/arxiv.1003.5993

29 pages

arxiv created 2010/03/31 · arxiv updated 2010/04/01

Abstract

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_1,3,13 with three zeros α, α³, and α¹³ of length 2^m-1 and the weight divisibility of its dual code are studied, where m≥ 5 is odd and α is a primitive element of the finite field \mathbbF_2^m. The code C_1,3,13 is proven to have the same weight distribution as the binary triple-error-correcting primitive BCH code C_1,3,5 of the same length.

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• New Families of Triple Error Correcting Codes with BCH Parameters
• Cyclic and BCH Codes whose Minimum Distance Equals their Maximum BCH bound
• On the weight distributions of several classes of cyclic codes from APN monomials
• A Class of Three-Weight Cyclic Codes