Issue No. 09 - September (1970 vol. 19)
K.W. Henderson , Stanford Linear Accelerator Center1 Stanford University
The matrix form of the Walsh functions as defined in the above-mentioned short note  can be generated by the modulo-2 product of two generating matrices: the natural binary code, and the transpose of the bit-reversed form of the first. As a result, the coefficients of the Walsh transform occur in bit-reversed order. By simply reordering the Walsh functions themselves to correspond to generation by the product of two such code matrices, neither or both in bit-reversed form, the Walsh coefficients occur in their natural order.
Code matrix, Walsh-Fourier transform, Walsh functions, Walsh matrix.
K.W. Henderson, "Comment on "Computation of the Fast Walsh-Fourier Transform"", IEEE Transactions on Computers, vol. 19, no. , pp. 850-851, September 1970, doi:10.1109/T-C.1970.223054