Abstract
Conditions on the existence of self-dual θ-codes defined over a finite field IFq are studied for θ automorphism of IFq. When q ≡ 1 (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.
Cite
CITATION STYLE
Boucher, D. (2015). A note on the existence of self-dual skew codes over finite fields. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9084, pp. 228–239). Springer Verlag. https://doi.org/10.1007/978-3-319-18681-8_18
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