1.	Suppose you create a binary code by appending to each message word a1 a2 a3 a4 three parity check digits c1 = a1 + a2 + a4, c2 = a2 + a3 + a4, and c3 = a2 + a3 + a4.  Will the resulting code detect and/or correct all single-digit errors? 	

2.	Suppose you create a binary code by appending to each message word a1 a2 a3  two parity check digits c1 = a1 + a2 and c2 = a2 + a3.  Will the resulting code detect and/or correct all single-digit errors? 	

3.	Suppose you create a binary code by appending to each message word a1 a2 a3  three parity check digits c1 = a1 + a2 , c2 = a2 + a3, and c3 = a1 + a3.  Will the resulting code detect and/or correct all single-digit errors? 	

4.	Append a fourth check digit to each seven-digit code created by the Venn Diagram method, c4 = a1 + a2 + a3 + a4.  With this additional check digit, can double errors be detected and/or corrected? 	

5.	For the message word a1 a2 a3 a4 , append four check digits:  c1 = a1, c2 = a2, c3 = a3, and c4 = a4.  Will the resulting code detect and/or correct all single-digit errors?  Can double errors be detected and/or corrected? 	

6.	Construct a code for five-digit binary message words that has four parity check digits.  Can it detect and/or correct single-digit errors? 	

7.	Construct a code for five-digit binary message words that has three parity check digits.  Can it detect and/or correct single-digit errors? 	

8.	Create a binary linear code with eight possible code words that can detect and correct any single-digit error. 	

9.	Create a binary linear code with four possible code words that can detect and correct any single-digit or double-digit error. 	

10.	Give an example of a circumstance where the code C = {00000, 11111} could be of use. 	

11.	Use the Caesar cipher to encrypt the message ABANDON HOPE. 	

12.	Use the Caesar cipher to decrypt the message DOO LV ZHOO. 	

13.	How does the weight of a code compare to the number of errors that can be detected? 	

14.	How does the weight of a code compare to the number of errors that can be corrected? 	

15.	Using modular arithmetic, determine (42·17) mod 23. 	

16.	Using modular arithmetic, determine (16·31) mod 41. 	

17.	Using modular arithmetic, determine 127 mod 53. 	

18.	Using modular arithmetic, determine 177 mod 41. 	

19.	Determine the value of s so that 9s = 1 mod 17. 	

20.	Determine the value of s so that 11s = 1 mod 13. 	

21.	For the RSA scheme with p = 5, q = 11, choose a value for r.  Then encode the message sent for the string "23." 	

22.	For the RSA scheme selected above, decode the message "7," if possible. 	

23.	For the RSA scheme with p = 17, q = 23, choose a value for r.  Then encode the message sent for the string "13." 	

24.	For the RSA scheme selected above, decode the message "7," if possible. 	

25.	Why is RSA considered a superior encryption scheme? 	

26.	Add the pair of binary sequences 1101001 and 1010011. 	

27.	Add the pair of binary sequences 1001010 and 1010010. 	

28.	Use the Vigenere cipher with the key word SPRING to encrypt the message APRIL SHOWERS. 	

29.	Given that TROUT was used as the key word to encrypt ZFBY YBJVCGZ with the Vigenere cipher, decrypt the message. 	

30.	Use the nearest-neighbor Venn diagram method to decode the received word 1011000. 	

31.	Construct the truth table for ¬(P Ù Q).	

32.	Construct the truth table for ¬(P Å Q).	

33.	Construct the truth table for ¬P Å ¬Q.	

Answer Key

1.	Detects all singles, doesn't correct all.	
2.	Detects all singles, doesn't correct all.	
3.	Yes.  Weight is 3.	
4.	Yes.  Weight is 4.	
5.	Detects all single errors, doesn't correct all.  Does not detect all double digit errors.	
6.	For example, c1 = a1 + a2 ; c2 = a2 + a3 ; c3 = a3 + a4 ; c4 = a4 + a5.  Detects all singles, doesn't correct all.	
7.	For example, c1 = a1 + a2 + a3 ; c2 = a2 + a3 + a4 ; c3 = a3 + a4 + a5.  Detects all singles, doesn't correct all.	
8.	For example, {111000000, 000111000, 000000111, 111000111, 111111000, 000111111, 111111111, 000000000}.	
9.	For example, {11111111, 11110000, 00001111, 00000000}.	
10.	It detects and corrects all single and double errors.	
11.	DEDQGRQ KRSH	
12.	ALL IS WELL	
13.	If a code has weight t, then t-1 errors can be detected.	
14.	If a code has weight t, then if t is even, (t-2)/2 errors can be corrected; if t is odd, (t-1)/2 errors can be corrected.	
15.	1	
16.	4	
17.	45	
18.	13	
19.	2	
20.	6	
21.	For example, choose r = 3.  Then 233 mod 55 is 12.	
22.	As above, if r = 3 and m = 20, s = 7.  So 77 mod 55 is 28.	
23.	For example, if r = 7, then 137 mod 391 is 55.	
24.	If r = 7 and m = 176, then s = 25.  So 725 mod 391 is 44.	
25.	It is a public key scheme that is effectively impossible to break.	
26.	0111010	
27.	0001000	
28.	SEIQY YZDNMEY	
29.	GONE FISHING	
30.	1111	
31.	
	
32.	
	
33.