Bit permutations (oeis.org/A195665)

% code to calculate bit-permutations, here matrix M of size 120x32
% below calculations for OEIS A195665

num = 5 ;
fnum = factorial(num) ;
pnum = 2^num ;

Powtwo = zeros(1,num) ;
for m=1:num
    Powtwo(m) = 2^(m-1) ;
end

Perms = perms(Powtwo) ;  % all permutations
Perms = horz(sortrows(horz(Perms))) ;  % reverse colex

% matrix

M = zeros( fnum , pnum ) ;
for m=1:fnum
    M(m,1:pnum) = cv2wp( Perms(m,:) ) ;  % compression vector to Walsh permutation
end

% sequence

Fact = 1 ;  % when m reaches this factorial, the current row length will be applied the last time, than doubled
Count = 2 ;  % used to calculate the next Fact
Length = 2 ;  % current row length
S = [] ;
for m=1:fnum
    S = [ S M(m,1:Length) ] ;
    if m == Fact
        Fact = Fact * Count ;
        Count = Count + 1 ;
        Length = 2 * Length ;
    end
end

% b-file

B = '' ;
for m=1:length(S)
    B = [ B num2str(m-1) ' ' num2str(S(m)) '\n' ] ;
end
fid = fopen('bfile','wt');
fprintf(fid,char(B));
fclose(fid);