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

Abstract Let p be any odd prime number, m and s be arbitrary positive integers, and let F p m be the finite field of cardinality p m . Existing literature only determines the number of all (Euclidean) self-dual cyclic codes of length p s over finite chain ring R = F p m + u F p m ( u 2 = 0 ) , such as Dinh et al. (2018). Using some combinatorial identities, we obtain certain properties for Kronecker product of matrices over F p with a specific type. On that basis, we give an explicit representation and enumeration for all distinct self-dual cyclic codes of length p s over R . Moreover, we provide an efficient method to construct every self-dual cyclic code of length p s over R precisely.