Response to the following problem:
We know that cyclic codes for all possible values of (n, k) do not exist.
1. Give an example of an (n, k) pair for which no cyclic code exists (k
2. How many (10, 2) cyclic codes do exist? Determine the generator polynomial of one such code.
3. Determine the minimum distance of the code in part 2.
4. How many errors can the code in part 2 correct?
5. If this code is employed for transmission over a channel which uses binary antipodal signaling with hard decision decoding and the SNR per bit of the channel is γb = 3 dB, determine an upper bound on the error probability of the system.