--- /dev/null
+## 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} {} minpol (@var{v})
+##
+## Finds the minimum polynomial for elements of a Galois Field. For a
+## vector @var{v} with @math{N} components, representing @math{N} values
+## in a Galois Field GF(2^@var{m}), return the minimum polynomial in GF(2)
+## representing thos values.
+## @end deftypefn
+
+function r = minpol (v)
+
+ if (nargin != 1)
+ error("usage: r = minpol(v)");
+ endif
+
+ if (!isgalois(v))
+ error("minpol: argument must be a galois variable");
+ endif
+
+ if (min (size (v)) > 1 || nargin != 1)
+ usage ("minpol (v), where v is a galois vector");
+ endif
+
+ n = length (v);
+ m = v.m;
+ prim_poly = v.prim_poly;
+ r = zeros(n,m+1);
+
+ ## Find cosets of GF(2^m) and convert from cell array to matrix
+ cyclocoset = cosets(m, prim_poly);
+ cyclomat = zeros(max(size(cyclocoset)),m);
+ for j=1:max(size(cyclocoset))
+ cyclomat(j,1:length(cyclocoset{j})) = cyclocoset{j};
+ end
+
+ for j =1:n
+ if (v(j) == 0)
+ ## Special case
+ r(j,m-1) = 1;
+ else
+ ## Find the coset within which the current element falls
+ [rc, ignored] = find(cyclomat == v(j));
+
+ rv = cyclomat(rc,:);
+
+ ## Create the minimum polynomial from its roots
+ ptmp = gf([1,rv(1)], m, prim_poly);
+ for i=2:length(rv)
+ ptmp = conv(ptmp, [1,rv(i)]);
+ end
+
+ ## Need to left-shift polynomial to divide by x while can
+ i = 0;
+ while (!ptmp(m+1-i))
+ i = i + 1;
+ end
+ ptmp = [zeros(1,i), ptmp(1:m+1-i)];
+ r(j,:) = ptmp;
+ endif
+ end
+
+ ## Ok, now put the return value into GF(2)
+ r = gf(r,1);
+
+endfunction