Euclidean and Hermitian Self-orthogonal Algebraic Geometry Codes and Their Application to Quantum Codes
Information Theory
2013-08-19 v1 math.IT
Abstract
In the present paper, we show that if the dimension of an arbitrary algebraic geometry code over a finite field of even characters is slightly less than half of its length, then it is equivalent to an Euclidean self-orthogonal code. However, in the literatures, a strong contrition about existence of certain differential is required to obtain such a result. We also show a similar result on Hermitian self-orthogonal algebraic geometry codes. As a consequence, we can apply our result to quantum codes and obtain quantum codes with good asymptotic bounds.
Cite
@article{arxiv.1308.3575,
title = {Euclidean and Hermitian Self-orthogonal Algebraic Geometry Codes and Their Application to Quantum Codes},
author = {Lingfei Jin and Chaoping Xing},
journal= {arXiv preprint arXiv:1308.3575},
year = {2013}
}