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Construction and enumeration for self-dual cyclic codes of even length over F2m + uF2m

Authors: 

Yuan Cao, Yonglin Cao∗, Hai Q. Dinh, Fang-Wei Fu, Fanghui Ma

Source title: 
Finite Fields and Their Applications, 61: 101598, 2020 (ISI)
Academic year of acceptance: 
2019-2020
Abstract: 

Let a be a finite field of cardinality a and a 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 a of length 2sn 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 a of length 2s+1can be obtained from self-dual cyclic code over a of length 2sn and by a Gray map preserving orthogonality and distances from a onto a.