gfrootod.m

数字通信第四版原书的例程

function [rt, rt_tp, alph] = gfrootod(f, ord, p)
%GFROOTOD Finds roots for GF(p) polynomial f(X) in the field GF(p^ord) 
%       (This is an old version of GFROOTS.)
%
%       RT = GFROOTS(F) finds all roots RT for GF(2) polynomial F(X) in the
%       GF(2^ORD), where ORD is the degree of polynomial F(X). The default
%       polynomial generating GF(2^ORD) is defined in GFPRIMDF.
%
%       RT = GFROOTS(F, ORD) finds all roots RT for GF(2) polynomial F(X) in
%       GF(2^ORD). GF(2^ORD) is a field generated by the default degree ORD
%       primitive polynomial, where ORD is a positive integer. ORD should be
%       larger or equals to the degree of F(X). When ORD is a vector in GF(2)
%       instead of a positive number, ORD is a primitive polynomail generated
%       GF(2^DEG), where DEG is the degree of ORD(X). DEG should be greater
%       than the degree of F(X). The output roots RT is an column vector with
%       a length equals to the degree of F(X). RT = [i, j, ..., k] means that
%       the roots of F(X) are the elements alpha^i, alpha^j, ..., alpha^k
%       in GF(2^ORD). The list of GF(P^ORD) can be found by using 
%       [tp, idx] = gftuple([-1:P^ORD], ORD, P)
%       This function outputs only the distinct roots of the polynomial F(X)
%       in the field.
%
%       RT = GFROOTS(F, ORD) finds all roots RT for GF(P) polynomial F(X) in
%       GF(P^ORD).
%
%       [RT, RT_TUPLE] = GFROOTS(...) outputs the roots RT and the M-tuple of
%       of RT. Each row of RT_TUPLE represents the ORD-tuple representation
%       of RT.
%
%       [RT, RT_TUPLE, ALPH] = GFROOTS(...) outputs the ORD-tuple of all
%       powers generated by the primitive polynomial.
%
%       See also: gfrepcov, hammgen, gfprimdf, gftuple.

%      Wes Wang 6/27/94.
%      Copyright (c) 1995-96 by The MathWorks, Inc.
%      $Revision: 1.1 $  $Date: 1996/04/01 17:59:51 $

% routine check
if nargin < 1
    error('Not enough input variable in calling GFROOTS.')
elseif nargin < 2
    ord = length(f) - 1;
end;
if nargin < 3
    p = 2;
end;

if length(ord) > 1
    dim = length(ord) - 1;
else
    dim = ord;
    ord = gfprimdf(dim, p);
end;
length_alph = p^dim;

% a list of all elements in GF(P^DIM)
alph = gftuple([-1 : length_alph - 2]', ord, p);

length_f = length(f);
rt = [];
rt_tp = [];
i = 1;

while((i <= length_alph) & (length(rt) < length_f))
  if i==1
    tmp = f(1);
  elseif i==2
    tmp = rem(sum(f), p);
  else
    tmp = [f(1) zeros(1,dim-1)];
    for j = 2 : length_f
        if f(j) ~= 0
            k = (i - 2) * (j - 1) + 2;
            if k > length_alph
                k = rem(k - 2, length_alph - 1) + 2;
            end
            tmp = gfadd(tmp, alph(k,:) * f(j), p);
        end;
    end;
  end;
  if max(tmp) == 0
      rt = [rt i];
      rt_tp = [rt_tp; alph(i,:)];
  end;
  i = i + 1;
end;
rt = rt(:) - 2;
ind = find(rt < 0);
if ~isempty(ind)
    rt(ind) = Inf * rt(ind);
end
%--end of GFROOTod.m--