On QC and GQC algebraic geometry codes
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911422351409152 |
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| author | Bonini, Matteo Dionigi, Arianna Ghiandoni, Francesco |
| author_facet | Bonini, Matteo Dionigi, Arianna Ghiandoni, Francesco |
| contents | We present new constructions of quasi-cyclic (QC) and generalized quasi-cyclic (GQC) codes from algebraic curves. Unlike previous approaches based on elliptic curves, our method applies to curves that are Kummer extensions of the rational function field, including hyperelliptic, norm-trace, and Hermitian curves. This allows QC codes with flexible co-index. Explicit parameter formulas are derived using known automorphism-group classifications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_05097 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On QC and GQC algebraic geometry codes Bonini, Matteo Dionigi, Arianna Ghiandoni, Francesco Information Theory Algebraic Geometry We present new constructions of quasi-cyclic (QC) and generalized quasi-cyclic (GQC) codes from algebraic curves. Unlike previous approaches based on elliptic curves, our method applies to curves that are Kummer extensions of the rational function field, including hyperelliptic, norm-trace, and Hermitian curves. This allows QC codes with flexible co-index. Explicit parameter formulas are derived using known automorphism-group classifications. |
| title | On QC and GQC algebraic geometry codes |
| topic | Information Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2602.05097 |