Using only the Hamming, Singleton and Gilbert-Varshamov bounds,

what is the most which can be said about the best possible value of M

for codes:

(a) defined over ZlO with n = 10, d = 5;

(b) defined over Z3 with n = 5, d = 3;

(c) defined over Z3 with n = 5,d = 47 Explain why the Hamming bound gives the same result for

(b) and (c).

In

(b) improve the lower bound for the best M by actually constructing a suitable code.