New families of quantum stabilizer codes from Hermitian self-orthogonal algebraic geometry codes
share
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.
READ FULL TEXT