Quantum MDS codes from BCH constacyclic codes

One central theme in quantum error correction is to construct quantum codes that have large minimum distances. It has been a great challenge to construct new quantum maximum-distance-separable (MDS) codes. Recently, some quantum MDS codes have been constructed from constacyclic codes. Under these constructions, one of the most important problems is to ensure these constacyclic codes are Hermitian dual-containing. This paper presents a method for determining the maximal designed distance of $$[[n, k, d]]_q$$[[n,k,d]]q quantum MDS codes from constacyclic codes with fixed n and q. From the method, we can get not only those known quantum MDS codes from constacyclic codes but also a new class of quantum MDS code from Hermitian dual-containing MDS constacyclic code.

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