Need solution of question 8. Please explain steps.

# 6 By the sphere ofradus k about a codeword a we mean the set of all words in Bn whose distance from a is no greater than k. This set is denoted by S(a); hence If t m 1), prove that any two spheres of radius t, say S(a) and S(b), have no elements in common. HINT: Assume there is a word x such that x E S(a) and x S,(b). Using the definitions of t and m, show that this is impossible.] 7 Deduce from part 6 that if there are t or fewer errors of transmission in a codeword, the received word will be decoded correctly 8 Let C2 be the code described in part 2. (If you have not yet found the minimum distance in C2, do so now.) Using the results of parts 5 and 7, explain why two errors in any codeword can always be detected, and why one error in any codeword can always be corrected