arXiv subjects

Farzaneh Ghanbari

Publications and source records attributed to Farzaneh Ghanbari.

3 recordsLinked to original sources

arXiv2025

Goppa code and quantum stabilizer codes from plane curves given by separated polynomials

In this paper, we examine algebraic geometric (AG) codes associated with curves generated by separated polynomials, and we create AG codes and quantum stabilizer codes from these curves by varying their parameters. Our research involves a thorough examination of the curves' algebraic features as well as the creation of Goppa codes over them. Extending these findings, we create quantum stabilizer codes, revealing that quantum codes built from Hermitian self-orthogonal AG codes have acceptable parameters, improving the reliability and performance of communication networks.

math.AG↗

arXiv2024

The $a$-number of $y^n=x^m+x$ over finite fields

This paper presents a formula for $a$-number of certain maximal curves characterized by the equation $y^{\frac{q+1}{2}} = x^m + x$ over the finite field $\mathbb{F}_{q^2}$. $a$-number serves as an invariant for the isomorphism class of the $p$-torsion group scheme. Utilizing the action of the Cartier operator on $H^0(\mathcal{X}, Ω^1)$, we establish a closed formula for $a$-number of $\mathcal{X}$.

math.NT↗

arXiv2024

Goppa Codes: Key to High Efficiency and Reliability in Communications

In this paper, we study some codes of algebraic geometry related to certain maximal curves. Quantum stabilizer codes obtained through the self orthogonality of Hermitian codes of this error correcting do not always have good parameters. However, appropriate parameters found that the Hermitian self-orthogonal code quantum stabilizer code has good parameters. Therefore, we investigated the quantum stabilizer code at a certain maximum curve and modified its parameters. Algebraic geometry codes show promise for enabling high data rate transmission over noisy power line communication channels.

cs.IT↗