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cosets.m

## Copyright (C) 2002 David Bateman
##
## 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 2 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} {} cosets (@var{m}, @var{prim})
##
## Finds the elements of GF(2^@var{m}) with primitive polynomial
## @var{prim}, that share the same minimum polynomial. Returns a 
## cell array of the paratitioning of GF(2^@var{m}).
## @end deftypefn

function c = cosets(m, prim)

  if (nargin == 1)
    prim = 0; ## This flags to use default primitive
  elseif (nargin != 2)
    error ("usage: c = cosets (m [, prim])");
  endif

  n = 2^m-1;
  found = zeros(1,n);
  c{1} = gf(1,m,prim);
  found(1) = 1;
  nc = 2;
  f = glog(gf(1:n,m,prim));

  while ((!all(found)))
    t = find(!found);
    idx = f(t(find(f(t) == min(f(t).x)))).x;
    set = idx;
    r = rem(idx*2,n);
    while (r > idx)
      set =[set,r];
      r = rem(r*2,n);
    end
    c{nc} = gf(sort(gexp(gf(set,m,prim)).x),m,prim);
    found(c{nc}.x) = ones(1,length(c{nc}));
    nc = nc + 1;
  end

endfunction

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