AG codes and AG quantum codes from the GGS curve
Combinatorics
2017-07-18 v2 Information Theory
math.IT
Abstract
In this paper, algebraic-geometric (AG) codes associated with the GGS maximal curve are investigated. The Weierstrass semigroup at all -rational points of the curve is determined; the Feng-Rao designed minimum distance is computed for infinite families of such codes, as well as the automorphism group. As a result, some linear codes with better relative parameters with respect to one-point Hermitian codes are discovered. Classes of quantum and convolutional codes are provided relying on the constructed AG codes.
Keywords
Cite
@article{arxiv.1703.03178,
title = {AG codes and AG quantum codes from the GGS curve},
author = {Daniele Bartoli and Maria Montanucci and Giovanni Zini},
journal= {arXiv preprint arXiv:1703.03178},
year = {2017}
}