Multi-point Codes from the GGS Curves
Information Theory
2019-02-25 v4 math.IT
Abstract
This paper is concerned with the construction of algebraic geometric codes defined from GGS curves. It is of significant use to describe bases for the Riemann-Roch spaces associated with totally ramified places, which enables us to study multi-point AG codes. Along this line, we characterize explicitly the Weierstrass semigroups and pure gaps. Additionally, we determine the floor of a certain type of divisor and investigate the properties of AG codes from GGS curves. Finally, we apply these results to find multi-point codes with excellent parameters. As one of the examples, a presented code with parameters over yields a new record.
Cite
@article{arxiv.1706.00313,
title = {Multi-point Codes from the GGS Curves},
author = {Chuangqiang Hu and Shudi Yang},
journal= {arXiv preprint arXiv:1706.00313},
year = {2019}
}
Comments
24 pages. arXiv admin note: text overlap with arXiv:1607.05462