New infinite families of quantum symmetric and asymmetric codes are constructed. Several of these are MDS. The codes obtained are shown to have parameters which are better than previously known. A number of known codes are special cases of the codes given here.
The asymmetric CSS construction is extended to the Hermitian dual case. New infinite families of quantum symmetric and asymmetric codes are constructed. In particular, new quantum codes are obtained from binary BCH codes and MDS codes. These codes have known minimum distances and thus the relationship between the rate gain and minimum distance is given explicitly. The codes obtained are shown to have parameters better than those of previous codes. A number of known codes are special cases of the codes given here.
Recently, considerable works of literature have grown up around the theme of quantum error-correcting codes. Quantum convolutional maximum distance separable (MDS for brevity) codes and MDS asymmetric quantum codes often have better properties in long-distance quantum communications and asymmetric quantum channels. Within this writing, the authors utilized constacyclic codes in constructing three new kinds of MDS quantum convolutional codes and a class of MDS asymmetric quantum codes. These results are new in comparison with those presented in the existing publications on this subject.
It is an important task to construct quantum maximum-distance-separable (MDS) codes with good parameters. In the present paper, we provide six new classes ofq-ary quantum MDS codes by using generalized Reed–Solomon (GRS) codes and Hermitian construction. The minimum distances of our quantum MDS codes can be larger than2q+1. Three of these six classes of quantum MDS codes have longer lengths than the ones constructed in[1]and[2], hence some of their results can be easily derived from ours via the propagation rule. Moreover, some known quantum MDS codes of specific lengths can be seen as special cases of ours and the minimum distances of some known quantum MDS codes are also improved as well.