New entanglement-assisted quantum error-correcting codes from negacyclic codes

Authors：Chen, Xiaojing; Lu, Xingbo; Zhu, Shixin; Jiang, Wan; Wang, Xindi^*

Source：Designs, Codes, and Cryptography, 2023.

DOI：10.1007/s10623-023-01335-0

• EAQEC codes
• Negacyclic codes
• EAQMDS codes
• Defining set

Entanglement-assisted quantum error-correcting (EAQEC) codes are a generalization of quantum error-correcting (QEC) codes, which can be constructed from arbitrary classical linear codes by relaxing the dual-containing condition and by using preshared entangled states between the sender and the receiver. In this paper, we investigate EAQEC codes of length n = 2(q(2)+1)/a, where q is an odd prime power, a = m(2) + 1 and m is an odd integer. The resulting EAQEC codes are entanglement-assisted quantum maximum-distance-separable (EAQMDS) codes when the minimum distance d <= n+2/2.