  The concept of quasi-affine frame in Euclidean spaces was introduced to
obtain translation invariance of the discrete wavelet transform. We extend this
concept to a local field $K$ of positive characteristic. We show that the
affine system generated by a finite number of functions is an affine frame if
and only the corresponding quasi-affine system is a quasi-affine frame. In such
a case the exact frame bounds are equal. This result is obtained by using the
properties of an operator associated with two such affine systems. We
characterize the translation invariance of such an operator. A related concept
is that of co-affine system. We show that there do not exist any co-affine
frame in $L^2(K)$.
