Higher Hamming weights for locally recoverable codes on algebraic curves
Commutative Algebra
2016-05-25 v2 Information Theory
math.IT
Abstract
We study the locally recoverable codes on algebraic curves. In the first part of this article, we provide a bound of generalized Hamming weight of these codes. Whereas in the second part, we propose a new family of algebraic geometric LRC codes, that are LRC codes from Norm-Trace curve. Finally, using some properties of Hermitian codes, we improve the bounds of distance proposed in [1] for some Hermitian LRC codes. [1] A. Barg, I. Tamo, and S. Vlladut. Locally recoverable codes on algebraic curves. arXiv preprint arXiv:1501.04904, 2015.
Cite
@article{arxiv.1505.05041,
title = {Higher Hamming weights for locally recoverable codes on algebraic curves},
author = {Edoardo Ballico and Chiara Marcolla},
journal= {arXiv preprint arXiv:1505.05041},
year = {2016}
}