gfcosets.m

数字通信第四版原书的例程

function cs = gfcosets(m, p);
%GFCOSETS Produces cyclotomic cosets mod(P^M - 1) with a prime number P.
%       CS = GFCOSETS(M) produces cyclomotic cosets mod(2^M - 1). Each row
%       of the output CS contains equivalent elements in the modulus
%       calculation.
%
%       CS = GFCOSETS(M, P) produces cyclomotic cosets mod(P^M - 1) with
%       prime number P.
%       
%       Because the length of the cosets varies in the complete set, NaN is
%       used to fill out the extra space in order to make all variables
%       have the same length in the output matrix CS.
%
%       See also GFPRIMFD, GFROOTS, GFMINPOL.

%       Wes Wang 7/18/94, 10/5/95
%       Copyright (c) 1995-96 by The MathWorks, Inc.
%       $Revision: 1.1 $  $Date: 1996/04/01 17:58:19 $

% routine check
if nargin < 1
  error('Not enough input variable in calling GFCOSETS.')
elseif nargin < 2
        p = 2;
end;

% the cyclotomic coset containing s consists of 
%     {s, ps, p^2s,...p^(k-1)s}
% where k is the smallest positive integer such that s p^k = s.

i = 1;
n = p^m - 1;
cs = [];              % used for the output
ind = ones(1, n - 1);      % used for the registration of un-processed number.
while ~isempty(i)

    % to process the number have not been done before.
      ind(i) = 0;     % mark the registor
     s = i;
  v = s;
  pk = rem(p*s, n);       % the next candidator

   % build cyclotommic coset contening s=i
 while (pk > s)
          ind(pk) = 0;    % mark the registor
             v = [v pk];     % recruit the number
            pk = rem(pk * p, n);    % the next candidator
   end;

    % add the coset into cs
 [m_cs, n_cs] = size(cs);
        [m_v, n_v ]  = size(v);
 if (n_cs == n_v) | (m_cs == 0)
          cs = [cs; v];
   elseif (n_cs > n_v)
             cs = [cs; [v, ones(1, n_cs - n_v) * NaN]];
      else
            % this case should not be happen, in general.
           cs = [[cs, ones(m_cs, n_v - n_cs) * NaN]; v];
   end;
    i = min(find(ind == 1));        % the next number.
end;

% add the number "0" to the very first
[m_cs, n_cs] = size(cs);
cs = [[0, ones(1, n_cs - 1) * NaN]; cs];

%--end of GFCOSETS--