Self-orthogonal and self-dual codes from maximal curves
Information Theory
2025-01-29 v1 Algebraic Geometry
math.IT
Abstract
In the field of algebraic geometric codes (AG codes), the characterization of dual codes has long been a challenging problem which relies on differentials. In this paper, we provide some descriptions for certain differentials utilizing algebraic structure of finite fields and geometric properties of algebraic curves. Moreover, we construct self-orthogonal and self-dual codes with parameters satisfying is close to . Additionally, quantum codes with large minimum distance are also constructed.
Cite
@article{arxiv.2501.16343,
title = {Self-orthogonal and self-dual codes from maximal curves},
author = {Puyin Wang and Jinquan Luo},
journal= {arXiv preprint arXiv:2501.16343},
year = {2025}
}