Hesham M. al-Salman Nov 2001

12

Encoding Cyclic Codes

nEncoding can be done by multiplying the message polynomial
by the generating
polynomial g(x)
ne.g. for the mentioned (7, 4) code g(X) = 1+X+X3. The message 1001 in polynomial format is 1
+ X3. The resulting code word is
(1+X+X3) × (1 + X3) = 1 + X + X4 + X6 (1100101)