Cryptology and Coding Theory
Group Homework #2
Due Monday 25 September 2006
Adams Chapter 1 Problems: 1.12
Adams Chapter 2 Problems: 2.2, 2.5, 2.7, 2.9, 2.12
Nonbook 1:
a. Prove that the set of all even-weight binary vectors of length n is a linear code
of length n.
b. How many codewords are in this code? Explain.
c. What is the minimum distance of this code? Explain.
d. What is a generator matrix for this code? Explain.
Nonbook 2: Given a binary linear code, show that the extended code (obtained by
appending an overall parity check bit to each codeword) is also a linear code.
Bonus: 2.14
Please include a short report of how your group worked.