








n 
Encoding can be
done by multiplying



the message
polynomial by the



generating
polynomial g(x)



n 
e.g. for the
mentioned (7, 4) code g(X)


= 1+X+X^{3}.
The message 1001 in



polynomial
format is 1 + X^{3}. The



resulting code
word is (1+X+X^{3}) × (1 +



X^{3}) =
1 + X + X^{4} + X^{6 } (1100101)

