(q-ary codes for limited magnitude errors) (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 l = 3 er- rors. (b) (Systematic codes). Assume that the number of information digits is k = 4 and the digits are over 28. Find the number of check digits required to correct all limited magnitude l = 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 digitds have - 1 errors in all positions. Explain how the decoding is done. (q-ary codes for limited magnitude errors) (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 l = 3 er- rors. (b) (Systematic codes). Assume that the number of information digits is k = 4 and the digits are over 28. Find the number of check digits required to correct all limited magnitude l = 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 digitds have - 1 errors in all positions. Explain how the decoding is done