Application of constacyclic codes to entanglement-assisted quantum maximum distance separable codes

作者：Liu, Yang; Li, Ruihu^*; Lv, Liangdong; Ma, Yuena

来源：Quantum Information Processing, 2018, 17(8): 210.

DOI：10.1007/s11128-018-1978-7

• Entanglement-assisted quantum code
• Constacyclic code
• Defining set
• Quantum MDS code

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 c of pre-shared entanglement pairs required to construct an EAQECC from arbitrary linear codes. In this paper, let q be a prime power, we aim to construct new q-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 c 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.

• 出版日期2018-8
• 单位中国人民解放军空军工程大学