4PSK coherent-state signals can be narrow sense group covariant with respect to F4 by coding

The formula of the channel matrix for group co-variant signals for classical-quantum communication has been studied to calculate the channel matrix analytically. However, despite its importance, the formula derived previously cannot be applied to coded q-ary phase shift keying (PSK) signals by linear codes over an extension field F
_q
. To derive the formula for codes over F
_q
, we focus on the 4PSK signals coded by the codes over F
₄
. In the present paper, we propose a construction method of a code of length 2n over F
₄
from a code of length n. If the original code is a group code, the coded 4PSK signals by the constructed code is narrow sense group covariant.