New families of quantum stabilizer codes from Hermitian self-orthogonal algebraic geometry codes

10/02/2021

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by   Lin Sok, et al.

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There have been a lot of effort to construct good quantum codes from the classical error correcting codes. Constructing new quantum codes using Hermitian self-orthogonal codes seems to be a difficult problem in general. In this paper, Hermitian self-orthogonal codes are studied from algebraic function fields. Sufficient conditions for the Hermitian self-orthogonality of an algebraic geometry code are presented. New Hermitian self-orthogonal codes are constructed from projective lines, hyper-elliptic curves and Hermitian curves. As an application, new families of quantum stabilizer codes are provided. Additionally, six new families of MDS quantum codes are obtained.