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

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

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...

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Bibliographic Details
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
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Institution: Nanyang Technological University
Language: English
Description
Summary: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.

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