--- /dev/null
+## Copyright (C) 2007 Muthiah Annamalai <muthiah.annamalai@uta.edu>
+##
+## 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} {} systematize (@var{G})
+##
+## Given @var{G}, extract P partiy check matrix. Assume row-operations in GF(2).
+## @var{G} is of size KxN, when decomposed through row-operations into a @var{I} of size KxK
+## identity matrix, and a parity check matrix @var{P} of size Kx(N-K).
+##
+## Most arbitrary code with a given generator matrix @var{G}, can be converted into its
+## systematic form using this function.
+##
+## This function returns 2 values, first is default being @var{Gx} the systematic version of
+## the @var{G} matrix, and then the parity check matrix @var{P}.
+##
+## @example
+## @group
+## G=[1 1 1 1; 1 1 0 1; 1 0 0 1];
+## [Gx,P]=systematize(G);
+##
+## Gx = [1 0 0 1; 0 1 0 0; 0 0 1 0];
+## P = [1 0 0];
+## @end group
+## @end example
+##
+## @end deftypefn
+## @seealso{bchpoly,biterr}
+function [G,P]=systematize(G)
+ if ( nargin < 1 )
+ print_usage();
+ end
+
+ [K,N]=size(G);
+
+ if ( K >= N )
+ error('G matrix must be ordered as KxN, with K < N');
+ end
+
+ %
+ % gauss-jordan echelon formation,
+ % and then back-operations to get I of size KxK
+ % remaining is the P matrix.
+ %
+
+ for row=1:K
+
+ %
+ %pick a pivot for this row, by finding the
+ %first of remaining rows that have non-zero element
+ %in the pivot.
+ %
+
+ found_pivot=0;
+ if ( G(row,row) > 0 )
+ found_pivot=1;
+ else
+ %
+ % next step of Gauss-Jordan, you need to
+ % re-sort the remaining rows, such that their
+ % pivot element is non-zero.
+ %
+ for idx=row+1:K
+ if ( G(idx,row) > 0 )
+ tmp=G(row,:);
+ G(row,:)=G(idx,:);
+ G(idx,:)=tmp;
+ found_pivot=1;
+ break;
+ end
+ end
+ end
+
+ %
+ %some linearly dependent problems:
+ %
+ if ( ~found_pivot )
+ error('cannot systematize matrix G');
+ return
+ end
+
+ %
+ % Gauss-Jordan method:
+ % pick pivot element, then remove it
+ % from the rest of the rows.
+ %
+ for idx=row+1:K
+ if( G(idx,row) > 0 )
+ G(idx,:)=mod(G(idx,:)+G(row,:),2);
+ end
+ end
+
+ end
+
+ %
+ % Now work-backward.
+ %
+ for row=K:-1:2
+ for idx=row-1:-1:1
+ if( G(idx,row) > 0 )
+ G(idx,:)=mod(G(idx,:)+G(row,:),2);
+ end
+ end
+ end
+
+ %I=G(:,1:K);
+ P=G(:,K+1:end);
+ return;
+end