We propose a way of characterizing the algorithms computing a Walsh-Hadamard transform that consist of a sequence of arrays of butterflies (I2n−1⊗DFT2) interleaved by linear permutations. Linear permutations are those that map linearly the binary representation of its element indices. We also propose a method to enumerate these algorithms.
@article{arxiv.1710.08029,
title = {Characterizing and Enumerating Walsh-Hadamard Transform Algorithms},
author = {François Serre and Markus Püschel},
journal= {arXiv preprint arXiv:1710.08029},
year = {2017}
}