An infinite class of quantum codes derived from duadic constacyclic codes
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866929358773420032 |
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| author | Dastbasteh, Reza Martinez, Josu Etxezarreta Nemec, Andrew iOlius, Antonio deMarti Bofill, Pedro Crespo |
| author_facet | Dastbasteh, Reza Martinez, Josu Etxezarreta Nemec, Andrew iOlius, Antonio deMarti Bofill, Pedro Crespo |
| contents | We present a family of quantum stabilizer codes using the structure of duadic constacyclic codes over $\mathbb{F}_4$. Within this family, quantum codes can possess varying dimensions, and their minimum distances are lower bounded by a square root bound. For each fixed dimension, this allows us to construct an infinite sequence of binary quantum codes with a growing minimum distance. Additionally, we prove that this family of quantum codes includes an infinite subclass of degenerate codes. We also introduce a technique for extending splittings of duadic constacyclic codes, providing new insights into the minimum distance and minimum odd-like weight of specific duadic constacyclic codes. Finally, we provide numerical examples of some quantum codes with short lengths within this family. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_06504 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An infinite class of quantum codes derived from duadic constacyclic codes Dastbasteh, Reza Martinez, Josu Etxezarreta Nemec, Andrew iOlius, Antonio deMarti Bofill, Pedro Crespo Information Theory 94B05, 94B15 We present a family of quantum stabilizer codes using the structure of duadic constacyclic codes over $\mathbb{F}_4$. Within this family, quantum codes can possess varying dimensions, and their minimum distances are lower bounded by a square root bound. For each fixed dimension, this allows us to construct an infinite sequence of binary quantum codes with a growing minimum distance. Additionally, we prove that this family of quantum codes includes an infinite subclass of degenerate codes. We also introduce a technique for extending splittings of duadic constacyclic codes, providing new insights into the minimum distance and minimum odd-like weight of specific duadic constacyclic codes. Finally, we provide numerical examples of some quantum codes with short lengths within this family. |
| title | An infinite class of quantum codes derived from duadic constacyclic codes |
| topic | Information Theory 94B05, 94B15 |
| url | https://arxiv.org/abs/2312.06504 |