Abstract: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.
| Comments: | 18 pages |
| Subjects: | Information Theory (cs.IT) |
| MSC classes: | 94B60 |
| Cite as: | arXiv:2511.02813 [cs.IT] |
| (or arXiv:2511.02813v4 [cs.IT] for this version) | |
| https://doi.org/10.48550/arXiv.2511.02813 arXiv-issued DOI via DataCite |
From: Angelynn Alvarez [view email]
[v1]
Tue, 4 Nov 2025 18:37:07 UTC (58 KB)
[v2]
Thu, 20 Nov 2025 17:43:54 UTC (63 KB)
[v3]
Fri, 26 Dec 2025 23:57:36 UTC (65 KB)
[v4]
Thu, 21 May 2026 23:42:33 UTC (44 KB)
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