New entanglement-assisted quantum MDS codes with length $n=\frac{q^2+1}{10\mu }$

Abstract

In this work, by investigating the decomposition of the defining set of constacyclic codes, we obtain two types of q-ary entanglement-assisted quantum MDS(EAQMDS) codes with length $n=\frac{q^2+1}{10\mu }$, where m is a positive integer, q is an odd prime power such that $q=10\mu m+\nu$ or $q=10\mu m+10\mu -\nu$, and both $\mu$ and $\nu$ are odd with $10\mu =\nu ^2+1$ and $\nu \ge 3$. Some of which are minimum distance achieves $\frac{q}{2}+1$ or even greater than $\frac{q}{2}+1$. Moreover, comparing the parameters with those of all known EAQMDS codes, the q-ary EAQMDS codes exhibited here are not covered in the sense that their parameters are more general than the results what have been previously known in the literature.