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

• Main Authors: Sok, Lin, Ezerman, Martianus Frederic, Ling, San
• Other Authors: School of Physical and Mathematical Sciences
• Format: Conference or Workshop Item
• Language: English
• Published: 2024
• Subjects: Mathematical Sciences; Quantum codes; MDS code; Algebraic geometry code; Self-orthogonal code; Reed-solomon code
• Online Access: https://hdl.handle.net/10356/175000
• Institution: Nanyang Technological University

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.