Paper Info
Title
Application of constacyclic codes to entanglement-assisted quantum maximum distance separable codes
Abstract
The entanglement-assisted stabilizer formalism overcomes the dual-containing constraint of standard stabilizer formalism for constructing quantum codes. This allows ones to construct entanglement-assisted quantum error-correcting codes (EAQECCs) from arbitrary linear codes by pre-shared entanglement between the sender and the receiver. However, it is not easy to determine the number of pre-shared entanglement pairs required to construct an EAQECC from arbitrary linear codes. In this paper, let be a prime power, we aim to construct new -ary EAQECCs from constacyclic codes. Firstly, we define the decomposition of the defining set of constacyclic codes, which transforms the problem of determining the number into determining a subset of the defining set of underlying constacyclic codes. Secondly, five families of non-Hermitian dual-containing constacyclic codes are discussed. Hence, many entanglement-assisted quantum maximum distance separable codes with are constructed from them, including ones with minimum distance . Most of these codes are new, and some of them have better performance than ones obtained in the literature.
Year
DOI
Venue
2018
https://doi.org/10.1007/s11128-018-1978-7
Quantum Information Processing
Keywords
Field
DocType
Entanglement-assisted quantum code,Constacyclic code,Defining set,Quantum MDS code
Discrete mathematics,Quantum codes,Quantum,Quantum entanglement,Quantum mechanics,Separable space,Formalism (philosophy),Prime power,Physics
Journal
Volume
Issue
ISSN
17
8
1570-0755
Citations 
PageRank 
References 
2
0.39
19
Authors
4
Name
Order
Citations
PageRank
Yang Liu1254.58
Ruihu Li2346.11
Liangdong Lv320.39
Yuena Ma451.12