Cyclic codes are special linear block codes with one extra property; the codewords are cyclically shifted. In a cyclic code, if a codeword is cyclically shifted (rotated), the result is another codeword. For example, if 1011000 is a codeword and we cyclically left-shift, then 0110001 is also a codeword.

Shown below is how a codeword is generated using a dataword and a generator. The generator for encoding the added values (r₀, r₁ and r₂) requires a division operation, which has been shown in the next figure.

Your task is to simulate the encoder and the decoder for a codeword. If you are not able to write a set of programming codes, you may write a pseudocode (50 points).

Sender Receiver Dataword Encoder Decoder ataword Accept Decision logic Syndrome S2 S1 So Divisoir d3 d2 di do Shared Generator Checker Codeword Codeword Sender Receiver Dataword Encoder Decoder ataword Accept Decision logic Syndrome S2 S1 So Divisoir d3 d2 di do Shared Generator Checker Codeword Codeword