Construction and enumeration for self-dual cyclic codes of even length over F_2^m + uF_2^m

Let  be a finite field of cardinality  and  be positive integers such that n is odd. In this paper, we give an explicit representation for every self-dual cyclic code over the finite chain ring  of length 2^sn and provide a calculation method to obtain all distinct codes. Moreover, we obtain a clear formula to count the number of all these self-dual cyclic codes. As an application, self-dual and 2-quasi-cyclic codes over  of length 2^s+1n can be obtained from self-dual cyclic code over  of length 2^sn and by a Gray map preserving orthogonality and distances from  onto .