An explicit representation and enumeration for self-dual cyclic codes over $\mathbb{F}_{2^m}+u\mathbb{F}_{2^m}$ of length $2^s$
(1811.11018)Abstract
Let $\mathbb{F}{2m}$ be a finite field of cardinality $2m$ and $s$ a positive integer. Using properties for Kronecker product of matrices and calculation for linear equations over $\mathbb{F}{2m}$, an efficient method for the construction of all distinct self-dual cyclic codes with length $2s$ over the finite chain ring $\mathbb{F}{2m}+u\mathbb{F}{2m}$ $(u2=0)$ is provided. On that basis, an explicit representation for every self-dual cyclic code of length $2s$ over $\mathbb{F}{2m}+u\mathbb{F}{2m}$ and an exact formula to count the number of all these self-dual cyclic codes are given.
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