1. If three film critics listed their ratings of a film with thumbs up (U) or thumbs down (D)—for example, one outcome is UDU—and critic number 1’s rating is first, critic number 2’s rating is second, critic number 3’s rating is third—the number of possible outcomes is

2. A four-digit binary message was encoded using Table 17.1 and the message 1010010 was received. Using the nearest-neighbor method, the decoded four-digit message is __________________________.

3. Using the circle diagram in Figure 17.1 to encode the message 1011, the encoded message is

4. The distance between received words 1011001 and 1000101 is ______________________.

5. Using the nearest-neighbor method and the code in Table 17.2, the word 1110011 decodes as

6. The weight of the binary linear code {0000000, 0011111, 0101011, 0110100} is ___________.

7. If the two messages 0 and 1 are encoded as 000 and 111, respectively, the number of errors that the code can correct is

8. If a binary linear code has weight 4, the maximum number of errors that it will detect is _______________.

9. If every pair of code words differs in at least five positions, then nearest-neighbor decoding can decode words accurately that have

10. Using the encoding scheme , the string 010110 decodes as

11. Use delta encoding to compress the following numbers: .

12. Given that the following numbers were encoded using the delta function, determine the original numbers: .

13. Find the following values: ; ; .

14. Solve the equation .

15. The Caesar cipher would encrypt GO HOME NOW as

16. The permissible values for the key of a decimation cipher are ______________.

17. Use the decimation cipher with key 9 to encrypt the message RUN.

18. Describe the cipher obtained when the values and are used in the linear cipher formula .

19. If a message were encrypted using the decimation cipher with the key 9, what value would you use to decrypt it? (Answer this question without looking at Table 17.4.)

20. The name for the cipher obtained when the value is used in the linear cipher formula is

21. Using the Vigenère cipher and the keyword ADAM to decrypt EIEIO, we obtain

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22. Counting the permutation , how many permutations of 1, 2, 3 are there?

23. Given , find .

24. If is a permutation cipher involving 1, 2, 3, 4, 5, 6, what is the length of the plaintext blocks?

25. If a permutation of the integers 1, 2, 3, 4, 5 was to encode the message MEET THE BOSS AT NOON, what would the blocks be?

26. If the first word of a message to be encrypted using a Playfair cipher was FLEET, how would it be converted to pairs of letters?

27. If the first word of a message to be encrypted using a Playfair cipher was JET, how would it be converted to pairs of letters?

28. The sum of the binary strings 1011001 and 1001101 is __________.

29. If is a binary string of length 8, what string is ?

30. Let . Find a string such that .