On non-binary quantum repeated-root cyclic codes

Abstract

In this paper, based on the Steane's enlargement construction, three classes of non-binary quantum codes are constructed from classical repeated-root cyclic codes of length 2ps over 𝔽q with odd characteristic p. The exact minimum distances of these quantum codes are determined. This construction yields a quantum MDS code with parameters [[2p, 2p - 4, 3]]p and two good quantum codes with parameters [[2p, 2p - 7, 4]]p and [[2p, 2p - 10, 5]]p.