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Four classes of new entanglement-assisted quantum optimal codes
Journal of Applied Mathematics and Computing ( IF 2.2 ) Pub Date : 2021-03-13 , DOI: 10.1007/s12190-021-01523-y
Xiaojing Chen , Shixin Zhu , Wan Jiang , Binbin Pang

Entanglement-assisted quantum error-correcting codes (EAQECCs) provide a general framework for quantum code construction, which overcome certain self-orthogonal restriction. It becomes one main task in quantum error-correction to find EAQECCs with good parameters, especially entanglement-assisted quantum maximum distance separable (EAQMDS) codes. In this work, we construct four new families of EAQECC codes with flexible parameters in view of negacyclic codes. It is worth pointing out that those EAQECCs are EAQMDS codes when \(d\le (n+2)/2\). By exploring the selection of defining sets, the constructed EAQECCs possess larger minimum distance in contrast with the known results in the literatures.



中文翻译:

四类新的纠缠辅助量子最优码

纠缠辅助量子纠错码(EAQECC)为克服某些自正交限制的量子码构建提供了一个通用框架。寻找具有良好参数,尤其是纠缠辅助量子最大距离可分离(EAQMDS)码的EAQECC,成为量子纠错的一项主要任务。在这项工作中,我们针对负循环代码构造了四个具有灵活参数的EAQECC代码新家族。值得指出的是,当\(d \ le(n + 2)/ 2 \)时,那些EAQECC是EAQMDS代码。通过探索定义集的选择,与文献中的已知结果相比,构造的EAQECC具有更大的最小距离。

更新日期:2021-03-15
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