Four new families of quantum stabilizer codes from hermitian self-orthogonal MDS codes

Abstract

We construct codes from rational function fields and provide sufficient conditions for a rational algebraic geometry code to be Hermitian self-orthogonal. A method to embed such codes yields new families of Hermitian self-orthogonal MDS codes with large dimensions. Using the stabilizer formalism, we construct four new families of quantum MDS codes with parameters $[N, N-2 K, K+1]_{q}$. We give conditions on the length N and the values of K of the dimension N-2K. Parameter comparisons over small fields highlight the novelty of the quantum codes that we obtain.