A Note on the Existence of Self-Dual Skew Codes over Finite Fields

摘要

Conditions on the existence of self-dual θ-codes defined over a finite field F_q are studied for θ automorphism of F_q. When q ≡ l (mod 4) it is proven that there always exists a self-dual θ-code in any dimension and that self-dual θ-codes of a given dimension are either all θ-cyclic or all θ-negacyclic. When q ≡ 3 (mod 4), there does not exist a self-dual θ-cyclic code and a necessary and sufficient condition for the existence of self-dual θ-negacyclic codes is given.