New optimal asymmetric quantum codes constructed from constacyclic codes

Abstract

In this paper, we propose the construction of asymmetric quantum codes from two families of constacyclic codes over finite field [Formula: see text] of code length [Formula: see text], where for the first family, [Formula: see text] is an odd prime power with the form [Formula: see text] ([Formula: see text] is integer) or [Formula: see text] ([Formula: see text] is integer) and [Formula: see text]; for the second family, [Formula: see text] is an odd prime power with the form [Formula: see text] or [Formula: see text] ([Formula: see text] is integer) and [Formula: see text]. As a result, families of new asymmetric quantum codes [Formula: see text] with [Formula: see text] distance larger than [Formula: see text] 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 [Formula: see text]. Also, all the newly obtained asymmetric quantum codes are optimal according to the singleton bound for asymmetric quantum codes.