Problem 3. (40 points) - Topic: Cyclic codes. Performance of coded systems.Design a (6,2) cyclic code by choosing the shortest possible generator polynomial. (Use the result from Problem 2)1) Determine the generator matrix G (in the systematic form) for this code and find all possible codewords.2) How many errors can be corrected by this code?3) Find the syndrome polynomial if the received word is 101110.4) Compare the performance (BER) of the coded system with that of the same system using unco