A generalized reverse jacket transform

Abstract

Generalization of the well-known Walsh-Hadamard transform (WHT), namely center-weighted Hadamard transform (CWHT) and complex reverse-jacket transform (CRJT) have been proposed and their fast implementation and simple index generation algorithms have recently been reported. These transforms are of size 2/sup r//spl times/2/sup r/ for integral values or r, and defined in terms of binary radix representation of integers. In this paper, using appropriate mixed-radix representation of integers, we present a generalized transform called general reverse jacket transform (GRJT) that unifies all the three classes of transforms, WHT, CWHT, and CRJT, and is also applicable for any even length vectors, that is of size 2/sup r//spl times/2/sup r/. A subclass of GRJT which includes CRJT (but not CWHT) is applicable for finite fields and useful for constructing error control codes.