Euclidean and Hermitian Hulls of MDS Codes and Their Applications to EAQECCs

被引：68
|
作者：
Fang, Weijun [1 ,2 ,3 ,4 ]
Fu, Fang-Wei [3 ,4 ,5 ]
Li, Lanqiang [6 ]
Zhu, Shixin [6 ]
机构：
[1] Tsinghua Univ, Shenzhen Int Grad Sch, Shenzhen 518055, Peoples R China
[2] Tsinghua Univ, Peng Cheng Lab, PCL Res Ctr Networks & Commun, Shenzhen 518055, Peoples R China
[3] Nankai Univ, Chern Inst Math, Tianjin 300071, Peoples R China
[4] Nankai Univ, LPMC, Tianjin 300071, Peoples R China
[5] Nankai Univ, Tianjin Key Lab Network & Data Secur Technol, Tianjin 300071, Peoples R China
[6] Hefei Univ Technol, Sch Math, Hefei 230601, Peoples R China
来源：
IEEE TRANSACTIONS ON INFORMATION THEORY | 2020年 / 66卷 / 06期
基金：
中国国家自然科学基金;
关键词：
Linear codes; hulls; Hermitian hulls; MDS codes; generalized Reed-Solomon codes; entanglement-assisted quantum error-correcting codes (EAQECCs); ERROR-CORRECTING CODES; LINEAR CODES; QUANTUM; PERMUTATION; EQUIVALENT;
D O I：
10.1109/TIT.2019.2950245
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this paper, we construct several classes of maximum distance separable (MDS) codes via generalized Reed-Solomon (GRS) codes and extended GRS codes, where we can determine the dimensions of their Euclidean hulls or Hermitian hulls. It turns out that the dimensions of Euclidean hulls or Hermitian hulls of the codes in our constructions can take all or almost all possible values. As a consequence, we can apply our results to entanglement-assisted quantum error-correcting codes (EAQECCs) and obtain several new families of MDS EAQECCs with flexible parameters. The required number of maximally entangled states of these MDS EAQECCs can take all or almost all possible values. Moreover, several new classes of q-ary MDS EAQECCs of length n > q + 1 are also obtained.
引用
收藏
页码：3527 / 3537
页数：11
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