Question

(3) Let C = {000000000000, 001101000011, 110010111100, 111111111111} (a) (3 marks) For all pairs C1, C2 EC find wt(c +ca). (b) (3 marks) Find the greatest value t so that C is a t-error correcting code. Justify your response. (c) (3 marks) Find ce so that c was sent, r = 100010110100 was received, and no more than t errors were introduced during transmission. Justify your response.

Answer 1

3. we knol know that w+ (c) = The Number of - non-zero terms inc. Gilun (3 CEŞ 0.00 0.000000, oo joo00011, 1, 101100, 000000000000 Ooilo 10000 110010111100 111111111111 ch Now when wt lc, +(2) an Wt 10, + C2) = q. (i) when c = 22 =21 > Wt [C, tc,) - Wt 120,1 = W+19) = 0. Wt 19,+(2) = Wt:162) = 5. Wt (+(3) = W7103) 37. Wt [C, +14) = W+[Cy) = 12: Wt (ca +13) = Wt1111111111111) = 12. Wt 162 +C) =W17(11.0010111100) 7. Wt 163+14) = Wt 1001101000011) -5. (6) here cu = (₂+ Cz. so the Generator matrix Ġ S oo 11 01 0000117 III 0010111100

Iso we know that - d = min. {wz (1) ? CEC ? cto 7. 5. I know that a code with minimum distance d can corre ft [d-I] errors [?] dinotes the greatest intero less than or equal to s Big [3:53 = 3. Here' di = 5. so t =12] = [ ] = 2 . G - Too Yol Oooo 117 © Tololol oooo 1 1 o lo, o I i II 0 0 So, Parity chick matrix is H=11oIT loi Ilo , Io is identity matrix --0000-0 -P----00

Now G) Щ Giun r= - чоро ) Ио) оо. o Hot - o o ЕНоооок око aopЕРок ооооооо ооооо оооооо o o o o o o o oo) o o o o o o oo o o o o o o oo o o o o o o oo o o ooo o o o o o o oo o o o o oo o o o o o o Гоо o o o o o o o To o o o o o o oo. то о o — ооо — о — я огоо = (o141-11 01.11) Now we find the error Paterne such that Het ahot. Thəm c= x-e Ays Here by hand not possible to find e.