A data decoder includes a communication unit receiving a bit signal with encoded data; a first operation unit that bit shifts the bit signal by a first length, corresponding to a length of a spreading code used to encode the data, to generate a first operation stream; a second operation unit generating a second operation stream without the spreading code; a third operation unit that bit shifts the second operation stream by a second length to generate a third operation stream; a fourth operation unit generating a fourth operation stream from which the data is removed using the second operation stream and the third operation stream; and a polynomial generator that decodes the encoded data using the fourth operation stream.