Construction and enumeration for self-dual cyclic codes of even length over F2m + uF2m
Construction and enumeration for self-dual cyclic codes of even length over F2m + uF2m
Source title:
Finite Fields and Their Applications, 61: 101598,
2020
(ISI)
Academic year of acceptance:
2019-2020
Abstract:
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 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
of length 2s+1n can be obtained from self-dual cyclic code over
of length 2sn and by a Gray map preserving orthogonality and distances from
onto
.