Quantum MDS codes with new length and large minimum distance

• Published in: Discrete mathematics Vol. 347; no. 1; p. 113662
• Main Authors: Fang, Weijun, Wen, Jiejing, Fu, Fang-Wei
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.01.2024
• Subjects: Generalized Reed-Solomon codes; Hermitian self-orthogonal codes; Norm function; Quantum MDS codes; Trace function; Norm function; Generalized Reed-Solomon codes; Trace function; Hermitian self-orthogonal codes; Quantum MDS codes
• ISSN: 0012-365X; 1872-681X
• DOI: 10.1016/j.disc.2023.113662

According to the well-known CSS construction, constructing quantum MDS codes are extensively investigated via Hermitian self-orthogonal generalized Reed-Solomon (GRS) codes. In this paper, given two Hermitian self-orthogonal GRS codes GRSk1(A,vA) and GRSk2(B,vB), we propose a sufficient condition to ensure that GRSk(A∪B,vA∪B) is still a Hermitian self-orthogonal code. Consequently, we first present a new general construction of infinitely families of quantum MDS codes from known ones. Moreover, applying the trace function and norm function over finite fields, we give another two new constructions of quantum MDS codes with flexible parameters. It turns out that the forms of the lengths of our quantum MDS codes are quite different from previous known results in the literature. Meanwhile, the minimum distances of all the q-ary quantum MDS codes are bigger than q/2+1.