An explicit representation and enumeration for self-dual cyclic codes over F_2^m+uF_2^m of length 2^s

11/27/2018

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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 and s a positive integer. Using properties for Kronecker product of matrices and calculation for linear equations over F_2^m, an efficient method for the construction of all distinct self-dual cyclic codes with length 2^s over the finite chain ring F_2^m+uF_2^m (u^2=0) is provided. On that basis, an explicit representation for every self-dual cyclic code of length 2^s over F_2^m+uF_2^m and an exact formula to count the number of all these self-dual cyclic codes are given.