% realize a (31,25) RS encoding & decoding in GF(2^5)
% primitive polynomial in GF(2^5):  a^5=a^2+1
% generator polynomial g(x)=(x+a)(x+a^2)(x+a^3)(x+a^4)(x+a^5)(x+a^6)
% codeword length N=31
% information sequence length k=25
% maximum number of error-correcting t=3

% the table convert the powers of a to a decimal number
T=[1,2,4,8,16,5,10,20,13,26,17,7,14,28,29,31,27,19,3,6,12,24,21,15,30,25,23,11,22,9,18];

% the input information sequence
disp('輸入信息序列：')
m_xi=1:25
% press any key to continue, to view the results clearly
disp('Press any key to continue...')
pause
% sequence after encoding
disp('編碼輸出序列（發送序列）：')
t_x=rs_encode(m_xi)

disp('Press any key to continue...')
pause
% press any key to continue
disp('信道產生的錯誤位置：')
sitegen=[0 5 30]
disp('信道產生的錯誤數值：')
valuegen=[5 3 7]
num=length(valuegen);
disp('Press any key to continue...')
pause
% press any key to continue
% sequence received after channel
disp('接收序列')
r_x=rs_channel(t_x,num,sitegen,valuegen)
disp('Press any key to continue...')
pause
% press any key to continue
% sequence after decoding
m_xo=rs_decoder(r_x)
disp('Done!')