Application of the Cartier Operator in Coding Theory

Vahid Nourozi

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arXiv · 2401.01305

Application of the Cartier Operator in Coding Theory

Vahid Nourozi

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Abstract

The $a$-number is an invariant of the isomorphism class of the $p$-torsion group scheme. We use the Cartier operator on $H^0(\mathcal{A}_2,\Omega^1)$ 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.

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Vahid Nourozi. 2024-01-02. Application of the Cartier Operator in Coding Theory. https://arxiv.org/abs/2401.01305

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