An efficient method to construct self-dual cyclic codes of length [formula omitted] over [formula omitted

Abstract

Let p be any odd prime number, m and s be arbitrary positive integers, and let Fpm 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 R=Fpm+uFpm(u2=0), such as Dinh et al. (2018). Using some combinatorial identities, we obtain certain properties for Kronecker product of matrices over Fp 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.