Application of the Cartier Operator in Coding Theory
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929196247285760 |
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| author | Nourozi, Vahid |
| author_facet | Nourozi, Vahid |
| contents | The $a$-number is an invariant of the isomorphism class of the $p$-torsion group scheme. We use the Cartier operator on $H^0(\mathcal{A}_2,Ω^1)$ to find a closed formula for the $a$-number of the form $\mathcal{A}_2 = v(Y^{\sqrt{q}}+Y-x^{\frac{\sqrt{q}+1}{2}})$ where $q=p^s$ over the finite field $\mathbb{F}_{q^2}$. The application of the computed $a$-number in coding theory is illustrated by the relationship between the algebraic properties of the curve and the parameters of codes that are supported by it. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01305 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Application of the Cartier Operator in Coding Theory Nourozi, Vahid Information Theory The $a$-number is an invariant of the isomorphism class of the $p$-torsion group scheme. We use the Cartier operator on $H^0(\mathcal{A}_2,Ω^1)$ to find a closed formula for the $a$-number of the form $\mathcal{A}_2 = v(Y^{\sqrt{q}}+Y-x^{\frac{\sqrt{q}+1}{2}})$ where $q=p^s$ over the finite field $\mathbb{F}_{q^2}$. The application of the computed $a$-number in coding theory is illustrated by the relationship between the algebraic properties of the curve and the parameters of codes that are supported by it. |
| title | Application of the Cartier Operator in Coding Theory |
| topic | Information Theory |
| url | https://arxiv.org/abs/2401.01305 |