8 research outputs found
Some constructions of quantum MDS codes
We construct quantum MDS codes with parameters for all , . These codes are shown to exist by
proving that there are classical generalised Reed-Solomon codes which contain
their Hermitian dual. These constructions include many constructions which were
previously known but in some cases these codes are new. We go on to prove that
if then there is no generalised Reed-Solomon
code which contains its Hermitian dual. We also construct
an quantum MDS code, an quantum
MDS code and a quantum MDS code, which are the first
quantum MDS codes discovered for which , apart from the quantum MDS code derived from Glynn's code
New Quantum MDS codes from Hermitian self-orthogonal generalized Reed-Solomon codes
Quantum maximum-distance-separable (MDS for short) codes are an important
class of quantum codes. In this paper, by using Hermitian self-orthogonal
generalized Reed-Solomon (GRS for short) codes, we construct four new classes
of -ary quantum MDS codes. The -ary quantum MDS codes we construct have
larger minimum distances. And the minimum distance of these codes is greater
than . Furthermore, it turns out that our quantum MDS codes generalize
the previous conclusions.Comment: 19 pages, 2 table