Cyclic AG-Codes on the Hermitian Curve
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913029793251328 |
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| author | Aguglia, Angela Korchmáros, Gábor |
| author_facet | Aguglia, Angela Korchmáros, Gábor |
| contents | Cyclic AG-codes $C_L(D,G)$ on the Hermitian curve $H_q$ over $\mathbb{F}_{q^2}$ are constructed such that $G = m(P_2 + \ldots + P_q)$, where $2 \le m \le q-1$ and $\mathrm{supp}(G)$ is the intersection of $H_q$ with a chord $\ell$ minus two points $P_1, P_{q+1}$. The divisor $D = Q_1 + \ldots + Q_{q^2-1}$ consists of all $q^2 - 1$ points in a single orbit under the action of the (cyclic) 2-point stabilizer $Γ$ of $(P_1, P_{q+1})$ in $\mathrm{Aut}(H_q) = \mathrm{PGU}(3,q)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_12499 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Cyclic AG-Codes on the Hermitian Curve Aguglia, Angela Korchmáros, Gábor Algebraic Geometry 14H55, 11T71, 94B27 Cyclic AG-codes $C_L(D,G)$ on the Hermitian curve $H_q$ over $\mathbb{F}_{q^2}$ are constructed such that $G = m(P_2 + \ldots + P_q)$, where $2 \le m \le q-1$ and $\mathrm{supp}(G)$ is the intersection of $H_q$ with a chord $\ell$ minus two points $P_1, P_{q+1}$. The divisor $D = Q_1 + \ldots + Q_{q^2-1}$ consists of all $q^2 - 1$ points in a single orbit under the action of the (cyclic) 2-point stabilizer $Γ$ of $(P_1, P_{q+1})$ in $\mathrm{Aut}(H_q) = \mathrm{PGU}(3,q)$. |
| title | Cyclic AG-Codes on the Hermitian Curve |
| topic | Algebraic Geometry 14H55, 11T71, 94B27 |
| url | https://arxiv.org/abs/2604.12499 |