Question

Let (di, d2,... .dk) (w1, w2,..., wx)-0 (mod n) be an error detection scheme for the k-digit identification number did2 . . .dk, where 0 〈 di 〈 n. Prove that all transposition errors of two digits di and dj are detected if and only if gcd(ui-y,n) = 1 for i and j between 1 and k

Answer 1

v_0 when s = 0, and k = 0 a = -kv^3 a = dv/dt dt = 1/a dv integrating on bath sides integral^t dt = integral^v_v_0 1/kv^3 dv t = 1/k integral^v_v_0 v^-3 dv = -1/k [v^-2/-2]^v_v_0 t = 1/2k [1/v - 1/v_0] [2kt + 1/v_0] = 1/v rightarrow v = v_0/2v_0kt + 1 v = ds/dt ds = vdt integral^s_0 ds = integral^t_0 v_0/2v_0kt + 1 dt s = v_0 ln (2v_0kt + 1) /2v_0 k s = 1/2k ln (2v_0kt + 1