function GG = gengray(N,K)
% generate the N-ary Gray code of length K
% taken from http://nr.stic.gov.tw/ejournal/ProceedingA/v22n6/841-848.pdf
% http://en.wikipedia.org/wiki/Gray_code
% Guan, Dah-Jyu. "Generalized Gray Codes with Applications." Proc. Katl. Sci. Counc. Repub. Of China (A) 22 (1998): 841-848. [5]. 

GG = [];
g = [];
u = [];
n = [];
for i=0:N
    g(i+1) = 0;
    u(i+1) = 1;
    n(i+1) = K;
end

while ~g(N+1)
    %for j=N-1:-1:0
    %    fprintf('%d',g(j+1));
    %end
    str = '';
    for j=N-1:-1:0
        str = [str, num2str(g(j+1))];
    end
    %fprintf('%s\n',str);
    GG(end+1) = base2dec(str,K);
    
    i = 0;
    k = g(1) + u(1);
    while ( (k>=n(i+1)) | (k<0) )
        u(i+1) = -u(i+1);
        i = i+1;
        k = g(i+1) + u(i+1);
    end
    g(i+1) = k;
end

return