  The concept of super-wavelet was introduced by Balan, and Han and Larson over
the field of real numbers which has many applications not only in engineering
branches but also in different areas of mathematics. To develop this notion on
local fields having positive characteristic we obtain characterizations of
super-wavelets of finite length as well as Parseval frame multiwavelet sets of
finite order in this setup. Using the group theoretical approach based on coset
representatives, further we establish Shannon type multiwavelet in this
perspective while providing examples of Parseval frame (multi)wavelets and
(Parseval frame) super-wavelets. In addition, we obtain necessary conditions
for decomposable and extendable Parseval frame wavelets associated to Parseval
frame super-wavelets.
