New optimal asymmetric quantum codes from constacyclic codes

摘要

In this paper, we construct two classes of asymmetric quantum codes by using constacyclic codes. The first class is the asymmetric quantum codes with parameters [[q~2 + 1,q~2 + 1 - 2(t + k + 1), (2k + 2)/(2t + 2)]]_q~2 where q is an odd prime power,t, k are integers with 0 ≤ t ≤ k ≤ q-1/2, which is a generalization of [J. Chen, J. Li and J. Lin, Int. J. Theor. Phys. 53 (2014) 72, Theorem 2] in the sense that we do not assume that q ≡ 1 (mod 4). The second one is the asymmetric quantum codes with parameters [[q~2-1/2,q~2-1/2-t-k, (k+1)/(t+1)]]_q~2, where q ≥ 5 is an odd prime power, t, k are integers with 0 ≤ t ≤ k ≤ q - 1. The constructed asymmetric quantum codes are optimal and their parameters are not covered by the codes available in the literature.