Cyclic codes and some new entanglement-assisted quantum MDS codes

Entanglement-assisted quantum error correcting codes (EAQECCs) play a significant role in protecting information from decoherence and noise. In this work, we construct six families of new EAQECCs lengths $$n=(q^2+1)/a$$ , $$n=q^2+1$$ $$n=(q^2+1)/2$$ cyclic codes, where $$a=m^2+1$$ ( $$m\ge 1$$ is odd) q an odd prime power with the form $$a|(q+m)$$ or $$a|(q-m)$$ . Moreover, those are entanglement-assisted maximum distance separable (EAQMDS) when $$d\le (n+2)/2$$ particular, length studied more general method selecting defining set different others. Compared all previously known results, work have flexible parameters larger minimum distance. All these sense that their not covered by available literature.