An efficient method to construct self-dual cyclic codes of length p^s\n over mathbbF_p^m+u mathbbF_p^m

2019/07/14 by Yuan Cao, Cao, Yuan, Yonglin Cao +5
Computer Science · Engineering · #Cellular Automata and Applications #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1907.07107

openalex publication_date 2019/07/14 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

Let p be an odd prime number, mathbbF_p^m be a finite field of\ncardinality p^m and s a positive integer. Using some combinatorial\nidentities, we obtain certain properties for Kronecker product of matrices over\n mathbbF_p with a specific type. On that basis, we give an explicit\nrepresentation and enumeration for all distinct self-dual cyclic codes of\nlength p^s over the finite chain ring mathbbF_p^m+u mathbbF_p^m\n(u²=0). Moreover, We provide an efficient method to construct every\nself-dual cyclic code of length p^s over mathbbF_p^m+u mathbbF_p^m\nprecisely.\n

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