On the condition on classical codes to construct quantum error correcting codes for amplitude damping channel

The amplitude damping (AD) quantum channel is one of the models describing evolution of quantum states. Several constructions of quantum error correcting codes for the AD channel based on classical codes has been presented, and Shor et al. proposed a class of classical codes over F
₃
which are efficiently applicable to this construction. Recently, we succeeded to expand Shor's construction to that based on classical codes over F
₇
. In this study, we further expand our construction method to that based on classical codes over F
_p
where p is arbitrary odd prime.