Construction of New Entanglement-Assisted Quantum MDS Codes

被引：0
|
作者：
Wang P. [1 ]
Wang L.-Q. [1 ]
Zhu S.-X. [1 ]
机构：
[1] School of Mathematics, Hefei University of Technology, Anhui, Hefei
来源：
Tien Tzu Hsueh Pao/Acta Electronica Sinica | 2024年 / 52卷 / 01期
基金：
中国国家自然科学基金;
关键词：
cyclotomic coset; entanglement-assisted quantum error-correcting codes; maximum-distance-separable (MDS) codes; negacyclic codes;
D O I：
10.12263/DZXB.20220819
中图分类号：
学科分类号：
摘要：
Entanglement-assisted quantum error-correcting codes are the generalization of classical quantum error-correcting codes, which realize quantum communication by using pre-shared entangled states between the receiver and the sender. It is an interesting problem to construct entanglement-assisted quantum error-correcting codes with small pre-shared entangled states because of the extra cost of pre-shared entangled states. In this paper, a sufficient condition for a class of negacyclic codes over finite fields to be Hermitian dual-containing codes is given. Then based on the structural properties of cyclotomic cosets, the existence conditions of different number of pre-shared entangled states are determined, and some new entanglement-assisted quantum maximum-distance-separable (MDS) codes with small pre-shared entangled states are obtained by using the construction method of entanglement-assisted quantum error-correcting codes. © 2024 Chinese Institute of Electronics. All rights reserved.
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页码：288 / 297
页数：9
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