Negacyclic Codes of Length $2^mp^n$ Over Finite Fields

Let
$F_{q}$
be a finite field of odd order
$q$
. Let
$m$
be a positive integer such that
$X^{2^{m}}+1$
factors completely into degree-one factors in
$F_{q^{2}}[X]$
. The polynomial generators of all negacyclic codes of length
$2^{m}p^{n}$
over
$F_{q}$
are obtained, where
$p$
is an odd prime coprime to
$q$
.