Problem 7. How many binary words of length 7 are at

(a) at Hamming distance 7 from (1, 0, 1, 0, 1, 0, 1)?

(b) at Hamming distance 6 from (1, 0, 1, 0, 1, 0, 1)?

Problem 8. Is the code in Problem 1(c) equivalent to the 5-ary repetition code { (0, 0, 0, 0 , 0), (1, 1, 1, 1, 1), (2, 2, 2, 2, 2), (3, 3, 3, 3, 3), (4, 4, 4, 4, 4) }. of length 5? Supply a proof to justify your answer.

Problem 1.

(c) C = { (0, 1, 2, 3, 4), (1, 2, 3, 4, 0), (2, 3, 4, 0, 1), (3, 4, 0, 1, 2), (4, 0, 1, 2, 3) }. Here q = 5.