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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.02813 |
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| _version_ | 1866918517135114240 |
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| author | Bastos, Gustavo Terra Álvarez, Angelynn Williams, Cameron |
| author_facet | Bastos, Gustavo Terra Álvarez, Angelynn Williams, Cameron |
| contents | Quasi-cyclic codes have been recently employed in the constructions of quantum error-correcting codes. In this paper, we propose a construction of infinite families of quasi-cyclic codes over $\F_q$ which are self-orthogonal with respect to the Euclidean and Hermitian inner products. In particular, their dimension and a lower bound for their minimum distance are computed using their constituent codes defined over field extensions of $\mathbb{F}_q$. We also show that the lower bound for the minimum distance satisfies the square-root-like lower bound and also show how dual-containing and self-dual quasi-cyclic codes can arise from our construction. Using the CSS construction, we show the existence of quantum error-correcting codes with good parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_02813 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Construction of Infinite Families of Good Self-Orthogonal Quasi-Cyclic Codes Bastos, Gustavo Terra Álvarez, Angelynn Williams, Cameron Information Theory 94B60 Quasi-cyclic codes have been recently employed in the constructions of quantum error-correcting codes. In this paper, we propose a construction of infinite families of quasi-cyclic codes over $\F_q$ which are self-orthogonal with respect to the Euclidean and Hermitian inner products. In particular, their dimension and a lower bound for their minimum distance are computed using their constituent codes defined over field extensions of $\mathbb{F}_q$. We also show that the lower bound for the minimum distance satisfies the square-root-like lower bound and also show how dual-containing and self-dual quasi-cyclic codes can arise from our construction. Using the CSS construction, we show the existence of quantum error-correcting codes with good parameters. |
| title | A Construction of Infinite Families of Good Self-Orthogonal Quasi-Cyclic Codes |
| topic | Information Theory 94B60 |
| url | https://arxiv.org/abs/2511.02813 |