A New Class Of Q-ary Quantum MDS Codes

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(10)1 with a big minimum distance.An important method is constructing quantum DMS codes from Hermitian self-orthogonal linear MDS codes.Hence,many linear MDS codes can be applied in the construction of quantum MDS codes,such as Reed Solomon codes,cyclic codes,negacyclic codes,and constacyclic codes.Many q-ary quantum MDS codes of length(q-1)(q(10)1)m have been constructed.He et al.used points on the finite fields to directly give Hermitian self-orthogonal polynomial codes,and obtained quantum MDS codes with length(q-1)(q(10)1)m,where m is not a factor of q(10)1 or q-1.This paper generalizes the work of He et al,uses even factor of q(10)1 to give Hermitian self-orthogonal MDS polynomial codes,and obtain a class of quantum MDS codes.Then this paper combines the second methods to present a new class of quantum MDS codes with short length and big minimum distance.Finally,we consider the quantum MDS codes of He et al,presents concrete infinite families of these parameters of their quantum MDS codes,and gives some concrete examples.These concrete parameters can also be used in our new quantum MDS codes.