% -*- 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}