cyclpoly.m

本书是电子通信类的本科、研究生辅助教材

function pr = cyclpoly(n, k, fd_flag)
%CYCLPOLY  Finds cyclic generator polynomials in GF(2).
%       PR = CYCLPOLY(N, K) finds one cyclic generator polynomial for a given
%       codeword length N and message length K.
%
%       PR = CYCLPOLY(N, K, FD_FLAG) finds cyclic generator polynomial(s) for
%       a given code word length N and message length K. The flag FC_FLAG
%       means:
%       FD_FLAG = 'min'  find the minimum degree cyclic generator polynomial.
%       FD_FLAG = 'max'  find the maximum degree cyclic generator polynomial.
%       FD_FLAG = 'all'  do an exhaustive search for all cyclic generator 
%                        polynomials of the given degree.
%       FD_FLAG = L      find all cyclic generator polynomials with L terms.
%
%       If no cyclic generator polynomial is found provided the given 
%       condition, PR is an empty output. A cyclic generator polynomial is
%       an irreducible polynomial.
%
%       See also HAMMGEN, GFPRIMFD, CYCLGEN.

%       Wes Wang 6/23/94, 10/2/95
%       Copyright (c) 1995-96 by The MathWorks, Inc.
%       $Revision: 1.1 $  $Date: 1996/04/01 17:56:02 $

% with message length k and code word length n, the degree of the cyclic
% generator polynomial length is m = n-k.
m = n - k;

if m < 0
    error('Message length cannot be shorter than code word length');
elseif m == 0
    pr = 1;
elseif m == 1
    pr = [1 1];
elseif m >= 2
    pr = [];

    nn = 2^(m-1) - 1;
    pp = [1, zeros(1, n-1), 1];
    if nargin < 3
        % find one result and return
        for i = 1 : nn
            % try all of possibility
            test_bed = [1, fliplr(de2bi(i, m-1)), 1];
            [q, r] = gfdeconv(pp, test_bed);
            if max(r) == 0
                pr = [pr; test_bed];
                return;
            end;
        end;

    elseif isstr(fd_flag)
        fd_flag = lower(fd_flag);

        if fd_flag(1:2) == 'mi'
            % minimum term
            for j = 3 : m + 1
                for i = 1 : nn
                    % try all of possibility
                    test_bed = [1, fliplr(de2bi(i, m-1)), 1];
                    if sum(test_bed) == j
                        [q, r] = gfdeconv(pp, test_bed);
                        if max(r) == 0
                            pr = test_bed;
                            return;
                        end;
                    end;
                end;
            end

        elseif fd_flag(1:2) == 'ma'
            % maximum term
            for j = m+1 : -1 : 3
                for i = 1 : nn
                    % try all of possibility
                    test_bed = [1, de2bi(i, m-1), 1];
                    if sum(test_bed) == j
                        [q, r] = gfdeconv(pp, test_bed);
                        if max(r) == 0
                            pr = test_bed;
                            return
                        end;
                    end;
                end;
            end

        else
            for i = 1 : nn
                % exhaust search
                test_bed = [1, fliplr(de2bi(i, m-1)), 1];
                [q, r] = gfdeconv(pp, test_bed);
                if max(r) == 0
                    pr = [pr; test_bed];
                end;
            end;
            %sort based on the minimum number of terms
            if ~isempty(pr)
                [x, i] = sort(sum(pr'));
                pr = pr(i, :);
            end;
        end;

    else
        % fd_flag is a number

        for i = 1 : nn
            % try all of possibility
            test_bed = [1, fliplr(de2bi(i, m-1)), 1];
            if sum(test_bed) == fd_flag
                [q, r] = gfdeconv(pp, test_bed);
                if max(r) == 0
                    pr = [pr; test_bed];
                end;
            end;
        end;
    end;
end;

if isempty(pr)
    disp('No primitive polynomial has been found provided the given constrain');
end;

%--end of CYCLPOLY--