Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / communications-1.1.1 / minpol.m

diff --git a/octave_packages/communications-1.1.1/minpol.m b/octave_packages/communications-1.1.1/minpol.m
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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} {} 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