Year: 2025
Type: preprint
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 $[n, k, d]_{q^2}$ satisfying $k + d$ is close to $n$. Additionally, quantum codes with large minimum distance are also constructed.
Source: arXiv (Cornell University)
Authors: Wang, Puyin, Luo, Jinquan
Institution: Central China Normal University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4406937732