Constructing and expressing Hermitian self-dual cyclic codes of length p^s over F_pm + uF_pm

Let p be an odd prime and m and s positive integers, with m even. Let further F-pm be the finite field of pm elements and R = F-pm + uF(pm) (u(2) = 0). Then R is a finite chain ring of p(2m) elements, and there is a Gray map from R-N onto F-pm(2N) which preserves distance and orthogonality, for any positive integer N. It is an interesting approach to obtain self-dual codes of length 2N over F-pm by constructing self-dual codes of length N over R. In particular, it has been shown that one of the key problems in constructing self-dual repeated-root cyclic codes over R is to find an effective way to present precisely Hermitian self-dual cyclic codes of length p(s) over R. But so far, only the number of these codes has been determined in literature. In this paper, we give an efficient way of constructing all distinct Hermitian self-dual cyclic codes of length p(s) over R by using column vectors of Kronecker products of matrices with specific types. Furthermore, we provide an explicit expression to present precisely all these Hermitian self-dual cyclic codes, using binomial coefficients.