/usr/share/octave/packages/communications-1.1.1/reedmullergen.m is in octave-communications-common 1.1.1-1.
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##
## This program is free software; you can redistribute it and/or modify it under
## the terms of the GNU General Public License as published by the Free Software
## Foundation; either version 3 of the License, or (at your option) any later
## version.
##
## This program is distributed in the hope that it will be useful, but WITHOUT
## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
## details.
##
## You should have received a copy of the GNU General Public License along with
## this program; if not, see <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {} reedmullergen (@var{R},@var{M})
##
## Definition type construction of Reed Muller code,
## of order @var{R}, length @math{2^M}. This function
## returns the generator matrix for the said order RM code.
##
## RM(r,m) codes are characterized by codewords,
## @code{sum ( (m,0) + (m,1) + @dots{} + (m,r)}.
## Each of the codeword is got through spanning the
## space, using the finite set of m-basis codewords.
## Each codeword is @math{2^M} elements long.
## see: Lin & Costello, "Error Control Coding", 2nd Ed.
##
## Faster code constructions (also easier) exist, but since
## finding permutation order of the basis vectors, is important, we
## stick with the standard definitions. To use decoder
## function reedmullerdec, you need to use this specific
## generator function.
##
## @example
## @group
## G=reedmullergen(2,4);
## @end group
## @end example
##
## @end deftypefn
## @seealso{reedmullerdec,reedmullerenc}
function G=reedmullergen(R,M)
if ( nargin < 2 )
print_usage();
end
G=ones(1,2^M);
if ( R == 0 )
return;
end
a=[0];
b=[1];
V=[];
for idx=1:M;
row=repmat([a,b],[1,2^(M-idx)]);
V(idx,:)=row;
a=[a,a];
b=[b,b];
end
G=[G; V];
if ( R == 1 )
return
else
r=2;
while r <= R
p=nchoosek(1:M,r);
prod=V(p(:,1),:).*V(p(:,2),:);
for idx=3:r
prod=prod.*V(p(:,idx),:);
end
G=[G; prod];
r=r+1;
end
end
return
end
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