Quantum maximum-distance-separable (MDS) codes are an important class of quantum codes. In this paper, using constacyclic codes and Hermitain construction, we construct some new quantum MDS codes of the form $q=2am+t$ , $n=\frac{q^{2}+1}{a}$ . Most of these quantum MDS codes are new in the sense that their parameters are not covered be the codes available in the literature.Quantum maximum-distance-separable (MDS) codes are an important class of quantum codes. In this paper, using constacyclic codes and Hermitain construction, we construct some new quantum MDS codes of the form $q=2am+t$, $n=\frac{q^{2}+1}{a}$. Most of these quantum MDS codes are new in the sense that their parameters are not covered be the codes available in the literature.

arXiv:1803.07927Mar 20, 20185 citations

Pseudo-cyclic Codes and the Construction of Quantum MDS Codes

Shuxing Li, Maosheng Xiong, Gennian Ge

Constacyclic codes which generalize the classical cyclic codes have played important roles in recent constructions of many new quantum maximum distance separable (MDS) codes. However, the mathematical mechanism may not have been fully understood. In this paper, we use pseudo-cyclic codes, which is a further generalization of constacyclic codes, to construct the quantum MDS codes. We can not only provide a unified explanation of many previous constructions, but also produce some new quantum MDS codes.Constacyclic codes which generalize the classical cyclic codes have played important roles in recent constructions of many new quantum maximum distance separable (MDS) codes. However, the mathematical mechanism may not have been fully understood. In this paper, we use pseudo-cyclic codes, which is a further generalization of constacyclic codes, to construct the quantum MDS codes. We can not only provide a unified explanation of many previous constructions, but also produce some new quantum MDS codes.

IEEE Transactions on Information TheoryFeb 26, 201640 citations

q=2am+t

n=\frac{q^{2}+1}{a}

. Most of these quantum MDS codes are new in the sense that their parameters are not covered be the codes available in the literature.