An efficient method to construct self-dual cyclic codes of length p^s over F_p^m + uF_p^m

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