Construction of Maximal Entanglement EAQECCs of Distance 4 from Caps in Projective Space PG(r,4)

2017 International Conference on Network and Information Systems for Computers (ICNISC) Pub Date : 2017-04-01 DOI:10.1109/ICNISC.2017.00014

Qiang Fu, Rui Li, Liangdong Lv, Yang Liu

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Abstract

The entanglement-assisted (EA) formalism is a generalization of the standard stabilizer formalism, and it can transform arbitrary quaternary classical linear codes into entanglement-assisted quantum error correcting codes (EAQECCs) by using of shared entanglement between the sender and the receiver. Using a decomposition of the 126-cap in PG(5,4), we firstly constructed LCD n-cap with 6The entanglement-assisted (EA) formalism is a generalization of the standard stabilizer formalism, and it can transform arbitrary quaternary classical linear codes into entanglement-assisted quantum error correcting codes (EAQECCs) by using of shared entanglement between the sender and the receiver. Using a decomposition of the 126-cap in PG(5,4), we firstly constructed LCD n-cap with 6≤n≤120. From these LCD caps, we then derived the related maximal entanglement [[n, n-6,4;6]] EAQECCs. Finally, using LCD LCD subcaps of 126-cap obtained, we constructed maximal entanglement EAQECCs with parameters [[n, n-;k,4;k]] for 6≤k≤11.

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射影空间PG(r,4)中距离帽点4的最大纠缠EAQECCs的构造

纠缠辅助(EA)形式是标准稳定器形式的推广，它可以利用发送方和接收方之间共享的纠缠，将任意四元经典线性码转换为纠缠辅助量子纠错码。通过对PG(5,4)中的126-cap的分解，我们首先构造了具有6的LCD n-cap。纠缠辅助(EA)形式是标准稳定器形式的推广，它可以利用发送端和接收端之间的共享纠缠将任意四元经典线性码转换为纠缠辅助量子纠错码(EAQECCs)。通过对PG(5,4)中126-cap的分解，我们首先构造了6≤n≤120的LCD n-cap。然后，我们从这些LCD帽中推导出相关的最大缠结[[n, n-6,4;6]] EAQECCs。最后，利用得到的126-cap的LCD子cap，我们构造了参数为[[n, n-;k,4;k]]的最大纠缠EAQECCs，对于6≤k≤11。

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来源期刊

2017 International Conference on Network and Information Systems for Computers (ICNISC)

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