An efficient method to construct self-dual cyclic codes of length $p^s$ over $\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}$

Abstract

Let p be an odd prime number, F p m be a finite field of cardinality p m and s a positive integer. 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 the finite chain ring F p m +uF p m (u 2 = 0). Moreover, We provide an efficient method to construct every selfdual cyclic code of length p s over F p m + uF p m precisely.