Constructing and expressing Hermitian self-dual cyclic codes of length ps over Fpm+uFpm.

Let p be an odd prime and m and s positive integers, with m even. Let further F p m be the finite field of p m elements and R = F p m + u F p m ( u 2 = 0 ). Then R is a finite chain ring of p 2 m elements, and there is a Gray map from R N onto F p m 2 N 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 p m 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. [ABSTRACT FROM AUTHOR]