1. (q-ary codes for limited magnitude errors, non-wrap error model) (a) For this problem assume that the symbols are over Z8 = {0, 1,2,3,4,5,6,7}. Find the maximum number of non-systematic codewords with length n=2 that can correct any number of limited magnitude 1 = 3 er- rors. (b) (Systematic codes). Assume that the number of information digits is k = 4 and the digits are over Z8. Find the number of check digits required to correct all limited magnitude 1 = 3 errors. (c) For the above systematic code, suppose the given information word is (7246). Find the corresponding check digits. (d) Assume the above codeword was transmitted and the received in- formation word is (5134) and the received check digits have -1 errors in all positions. Explain how the decoding is done. 1. (q-ary codes for limited magnitude errors, non-wrap error model) (a) For this problem assume that the symbols are over Z8 = {0, 1,2,3,4,5,6,7}. Find the maximum number of non-systematic codewords with length n=2 that can correct any number of limited magnitude 1 = 3 er- rors. (b) (Systematic codes). Assume that the number of information digits is k = 4 and the digits are over Z8. Find the number of check digits required to correct all limited magnitude 1 = 3 errors. (c) For the above systematic code, suppose the given information word is (7246). Find the corresponding check digits. (d) Assume the above codeword was transmitted and the received in- formation word is (5134) and the received check digits have -1 errors in all positions. Explain how the decoding is done