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cosets.m    58 lines (50 with data), 1.7 kB

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## 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 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} {} 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
## partitioning 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)
print_usage ();
endif
n = 2^m-1;
found = zeros (1, n);
c{1} = gf (1, m, prim);
found(1) = 1;
nc = 2;
f = log (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);
endwhile
c{nc} = gf (sort (exp (gf (set, m, prim)).x), m, prim);
found(c{nc}.x) = ones (1, length (c{nc}));
nc = nc + 1;
endwhile
endfunction
%% Test input validation
%!error cosets ()
%!error cosets (1, 2, 3)