2000 character limit reached
Application of the Cartier Operator in Coding Theory (2401.01305v1)
Published 2 Jan 2024 in cs.IT and math.IT
Abstract: The $a$-number is an invariant of the isomorphism class of the $p$-torsion group scheme. We use the Cartier operator on $H0(\mathcal{A}_2,\Omega1)$ 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 $q=ps$ over the finite field $\mathbb{F}{q2}$. 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.
- V. Nourozi. The rank Cartier operator and linear system on curves= Classificação do operador Cartier e sistemas lineares na curva. Doctoral dissertation., 2021.
- V. Nourozi, and F. Ghanbari. Goppa code and quantum stabilizer codes from plane curves given by separated polynomials. arXiv preprint arXiv:2306.07833(2023).
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.
