New Galois Hulls of GRS Codes and Application to EAQECCs
Information Theory
2021-08-03 v3 math.IT
Abstract
Galois hulls of linear codes have important applications in quantum coding theory. In this paper, we construct some new classes of (extended) generalized Reed-Solomon (GRS) codes with Galois hulls of arbitrary dimensions. We also propose a general method on constructing GRS codes with Galois hulls of arbitrary dimensions from special Euclidean orthogonal GRS codes. Finally, we construct several new families of entanglement-assisted quantum error-correcting codes (EAQECCs) and MDS EAQECCs by utilizing the above results.
Keywords
Cite
@article{arxiv.2011.14061,
title = {New Galois Hulls of GRS Codes and Application to EAQECCs},
author = {Xiaolei Fang and Renjie Jin and Jinquan Luo and Wen Ma},
journal= {arXiv preprint arXiv:2011.14061},
year = {2021}
}