New optimal asymmetric quantum codes constructed from constacyclic codes

In this paper, we propose the construction of asymmetric quantum codes from two families of constacyclic codes over finite field 𝔽q2 of code length n, where for the first family, q is an odd prime power with the form 4t + 1 (t ≥ 1 is integer) or 4t − 1 (t ≥ 2 is integer) and n1 = q2+1 2; for the second family, q is an odd prime power with the form 10t + 3 or 10t + 7 (t ≥ 0 is integer) and n2 = q2+1 5. As a result, families of new asymmetric quantum codes [[n,k,dz/dx]]q2 with dz distance larger than q + 1 are obtained, which are not covered by the asymmetric quantum error-correcting codes (AQECCs) in Refs. 32 and 33 [J.-Z. Chen, J.-P. Li and J. Lin, Int. J. Theor. Phys. 53, 72 (2014); L. Wang and S. Zhu, Int. J. Quantum Inf. 12, 1450017 (2014)] that dz ≤ q + 1. Also, all the newly obtained asymmetric quantum codes are optimal according to the singleton bound for asymmetric quantum codes.