Improved Two-Point Codes on Hermitian Curves
Information Theory
2011-02-18 v2 Algebraic Geometry
math.IT
Number Theory
Abstract
One-point codes on the Hermitian curve produce long codes with excellent parameters. Feng and Rao introduced a modified construction that improves the parameters while still using one-point divisors. A separate improvement of the parameters was introduced by Matthews considering the classical construction but with two-point divisors. Those two approaches are combined to describe an elementary construction of two-point improved codes. Upon analysis of their minimum distance and redundancy, it is observed that they improve on the previous constructions for a large range of designed distances.
Keywords
Cite
@article{arxiv.1004.1752,
title = {Improved Two-Point Codes on Hermitian Curves},
author = {Iwan Duursma and Radoslav Kirov},
journal= {arXiv preprint arXiv:1004.1752},
year = {2011}
}