Extending self-orthogonal codes

Authors: ALP BASSA, NESRİN TUTAŞ

Abstract: In this short note we give an exact count for the number of self-dual codes over a finite field $\mathbb F_q$ of odd characteristic containing a given self-orthogonal code. This generalizes an analogous result of MacWilliams, Sloane, and Thompson over the field $\mathbb F_2$ to arbitrary odd finite fields $\mathbb F_q$.

Keywords: Symmetric bilinear forms, self-dual codes, maximal isotropic subspaces

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