English

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 [216,190,18] [216,190,\geqslant 18] over F64 \mathbb{F}_{64} 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

R2 v1 2026-06-22T20:06:19.894Z