Binary Walsh matrix in sequency order (compare this file) as a product

• White (0) and red (1): result with modulo 2 operations

• Gray numbers: result with normal operations

The two matrices used as factors (which are transposed to each other) correspond to the same Walsh permutation wp(6,9,1,10) = (0,6,9,15, 1,7,8,14, 10,12,3,5, 11,13,2,4).
All 48 Walsh permutations whose compression vectors are permutations of (1,6,9,10) or (2,5,13,14) could have been used instead.
wp(6,9,1,10) was chosen, because it is the only one with a symmetric compression matrix (shown in the top left corner).