New entanglement-assisted quantum MDS codes with length $n=\frac{q^2+1}5$

TL;DR

This paper constructs new entanglement-assisted quantum MDS codes of length (q^2+1)/5 from cyclic codes, offering more flexible parameters and larger minimum distances than previous codes of the same length.

Contribution

It introduces a novel method to construct EAQMDS codes with specific length from cyclic codes, expanding the known parameter sets.

Findings

Codes have larger minimum distances.

Codes exhibit flexible parameters.

Construction method is applicable to a new length.

Abstract

The entanglement-assisted stabilizer formalism can transform arbitrary classical linear codes into entanglement-assisted quantum error correcting codes (EAQECCs). In this work, we construct some new entanglement-assisted quantum MDS (EAQMDS) codes with length $n=\frac{q^2+1}5$ from cyclic codes. Compared with all the previously known parameters with the same length, all of them have flexible parameters and larger minimum distance.