On Jacket transforms over finite fields

In 2001 Lee, Rajan and Park introduced (among other things) the concept of extended complex reverse jacket (CRJ) transform over finite field. In this paper, we prove that this transform is equivalent to Galois field Fourier (GFF) transform and possesses an additional feature of having a matrix with specific border. We also, present examples of Jacket transforms over finite fields applicable to odd dimensions extending in this way previous works on the subject.