关于量子BCH码及子系统码二元构造的研究

On Quantum BCH Codes and a Binary Construction of Quantum Subsystem Codes

根据已有的关于二元本原经典BCH码的自同构群的结论,给出了一类特殊的量子BCH码自同构群的描述和量子CSS码码算子的描述。基于GF(4)上迹Hermitian内积和GF(2)上的辛内积之间的关系,给出了量子子系统码的一种二元构造方法,丰富了子系统码的构造方法。

We consider the automorphism group of the binary quantum primitive BCH codes based on some results of the automorphism group of binary primitive classical BCH codes. Besides this, we give the expression of the projector onto quantum CSS codes. Based on the relationship between trace Hermitian inner product over GF（4） and symplectic inner product over GF（2）, we give a binary construction of subsystem codes, which makes the construction of subsystem codes more various.