A generalized reverse jacket transform

Generalization of the well-known Walsh-Hadamard transform (WHT), namely cen ter-weighted Hadamard transform (CWHT) and complex reverse-jacket transform (CRJT) have been proposed and their fast implementation and simple index g eneration algorithms have recently been reported. These transforms are of s ize 2(r) x 2(r) for integral values or r, and defined in terms of binary ra dix representation of integers. In this paper, using appropriate mixed-radi x representation of integers, we present a generalized transform called gen eral reverse jacket transform (GRJT) that unifies all the three classes of transforms, WHT, CWHT, and CRJT, and also applicable for any even length ve ctors, that is of size 2r x 2r. A subclass of GRJT which includes CRJT (but not CWHT) is applicable for finite fields and useful for constructing erro r control codes.