Goppa code and quantum stabilizer codes from plane curves given by separated polynomials
Algebraic Geometry
2025-01-06 v3
Abstract
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.
Keywords
Cite
@article{arxiv.2306.07833,
title = {Goppa code and quantum stabilizer codes from plane curves given by separated polynomials},
author = {Vahid Nourozi and Farzaneh Ghanbari},
journal= {arXiv preprint arXiv:2306.07833},
year = {2025}
}