Elementary Constructions of Best Known Quantum Codes
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909351578435584 |
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| author | Aydin, Nuh Nguyen, Trang T. T. Tran, Long B. |
| author_facet | Aydin, Nuh Nguyen, Trang T. T. Tran, Long B. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_12167 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Elementary Constructions of Best Known Quantum Codes Aydin, Nuh Nguyen, Trang T. T. Tran, Long B. Information Theory Quantum Algebra 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. |
| title | Elementary Constructions of Best Known Quantum Codes |
| topic | Information Theory Quantum Algebra |
| url | https://arxiv.org/abs/2410.12167 |