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An efficient method to construct self-dual cyclic codes of length ps over Fp+ uFpm

Authors: 

Yuan Cao, Yonglin Cao, Hai Q. Dinh, Somphong Jitman

Source title: 
Discrete Mathematics, 343(6): 111868, 2020 (ISI)
Academic year of acceptance: 
2020-2021
Abstract: 

Let p be any odd prime number, m and s be arbitrary positive integers, and let a be the finite field of cardinality pm. Existing literature only determines the number of all (Euclidean) self-dual cyclic codes of length ps over finite chain ring a (u= 0), such as Dinh et al. (2018). Using some combinatorial identities, we obtain certain properties for Kronecker product of matrices over a with a specific type. On that basis, we give an explicit representation and enumeration for all distinct self-dual cyclic codes of length ps over R. Moreover, we provide an efficient method to construct every self-dual cyclic code of length ps over R precisely.