Permutation of the natural ordered Hadamard matrix into the sequency ordered Hadamard matrix of order 16
The former is usually referred to as Walsh matrix, but sometimes also the latter.
The number of sign changes per row in the natural ordered matrix is wp(15,7,3,1) = (0,15,  7,8,  3,12,  4,11,  1,14,  6,9,  2,13,  5,10){\displaystyle wp(15,7,3,1)~=~(0,15,~~7,8,~~3,12,~~4,11,~~1,14,~~6,9,~~2,13,~~5,10)},
in the sequency ordered matrix the number of sign changes is consequtive.
The permutation is the product of the Gray code permutation and the Bit-reversal permutation:
Own work
WatchduckYou can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck".