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 $$n=\\frac{q^2+1}{10\\mu }$$\n , where m is a positive integer, q is an odd prime power such that $$q=10\\mu m+\\nu $$\n or $$q=10\\mu m+10\\mu -\\nu $$\n , and both $$\\mu $$\n and $$\\nu $$\n are odd with $$10\\mu =\\nu ^2+1$$\n and $$\\nu \\ge 3$$\n . Some of which are minimum distance achieves $$\\frac{q}{2}+1$$\n or even greater than $$\\frac{q}{2}+1$$\n . 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.