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

07/14/2019

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by   Yuan Cao, et al.

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Let F_2^m be a finite field of cardinality 2^m, R=F_2^m+uF_2^m (u^2=0) and s,n 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 R 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 F_2^m of length 2^s+1n can be obtained from self-dual cyclic code over R of length 2^sn and by a Gray map preserving orthogonality and distances from R onto F_2^m^2.