Paper Info
Title
Some New Classes of Entanglement-Assisted Quantum MDS Codes Derived From Constacyclic Codes
Abstract
Although quantum maximal-distance-separable (MDS) codes that satisfy the quantum singleton bound have become an important research topic in the quantum coding theory, it is not an easy task to search for quantum MDS codes with the minimum distance that is larger than (q/2) + 1. The pre-shared entanglement between the sender and the receiver can improve the minimum distance of quantum MDS codes such that the minimum distance of some constructed codes achieves (q/2) + 1 or exceeds (q/2) + 1. Meanwhile, how to determine the required number of maximally entangled states to make the minimum distance of quantum MDS codes larger than (q/2) + 1 is an interesting problem in the quantum coding theory. In this paper, we utilize the decomposition of the defining set and q(2)-cyclotomic cosets of constacyclic codes with the form q = alpha m + t or q = alpha m + alpha - t and n = (q(2) + 1/alpha) to construct some new families of entanglement-assisted quantum MDS codes that satisfy the entanglement-assisted quantum singleton bound, where q is an odd prime power and m is a positive integer, while both alpha and t are positive integers such that alpha = t(2) + 1. The parameters of these codes constructed in this paper are more general compared with the ones in the literature. Moreover, the minimum distance of some codes in this paper is larger than (q/2) + 1 or q + 1.
Year
DOI
Venue
2019
10.1109/ACCESS.2019.2927294
IEEE ACCESS
Keywords
DocType
Volume
Entanglement-assisted quantum codes,constacyclic codes,maximal-distance-separable (MDS) codes
Journal
7
ISSN
Citations 
PageRank 
2169-3536
0
0.34
References 
Authors
0
5
Name
Order
Citations
PageRank
Jianzhang Chen181.46
Youqin Chen200.68
Chunhui Feng300.68
Yuanyuan Huang4275.77
Riqing Chen510831.00