This report presents the details and basic theory of the coding scheme employed on Mode S uplink and downlink transmissions. Since ATCRBS interference is the main source of error for these signals, a cyclic burst detection code was chosen for Mode S. This code permits simple error detection at the transponder and more complex error correction at the sensor. The theory behind cyclic encoding and decoding as used for Mode S is presented first. Then, since polynomial multiplication and division are required for these processes, circuits for these operations are described. Finally, the last chapter describes the actual implementations specified for encoding and decoding in both the transponder and sensor.