一类新的q元量子MDS码

A Class of New q-ary Quantum MDS Codes

量子纠错码在量子信息处理和量子计算中有着重要的应用.q元量子MDS码是一类重要的最优量子纠错码,此类量子码的参数满足相应的量子Singleton界.构造q元量子MDS码具有重要的理论和应用意义.但构造码长q+1的q元量子MDS码是比较困难的,许多码长(q+1)(q-1)/m的q元量子MDS码,其中m整除q+1或q-1,已经被构造出来.在HE Xiangming等构造出的q元量子MDS码的基础上,给出了几类q元量子MDS码的具体实例,这些量子MDS码具有码长(q+1)(q-1)/m,其中m整除(q+1)(q-1),但m不整除q-1,也不整除q+1.

Quantum codes have applications in quantum computing and quantum communications.Quantum maximal distance separable（MDS）codes are a class of optimal quantum error-correcting codes and their parameters satisfy the quantum Singleton bound.The construction of quantum MDS codes has important application in theory and practice.It is still difficult to construct q-ary quantum MDS codes of length bigger than q＋1with a big minimum distance.Many q-ary quantum MDS codes of length（q＋1）（q-1）/m have been constructed,where mis a factor of q＋1 or q-1.This paper uses some results in[20]and presents some quantum MDS codes of length（q＋1）（q-1）/m,where m is a factor of（q＋1）（q-1）,m is not a factor of q＋1or q-1.