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arXiv · 2410.12167

Elementary Constructions of Best Known Quantum Codes

Nuh Aydin·Trang T. T. Nguyen·Long B. Tran
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Abstract

Recently, many good quantum codes over various finite fields $F_q$ have been constructed from codes over extension rings or mixed alphabet rings via some version of a Gray map. We show that most of these codes can be obtained more directly from cyclic codes or their generalizations over $F_q$. Unless explicit benefits are demonstrated for the indirect approach, we believe that direct and more elementary methods should be preferred.

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Nuh Aydin, Trang T. T. Nguyen, Long B. Tran. 2024-10-16. Elementary Constructions of Best Known Quantum Codes. https://arxiv.org/abs/2410.12167

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