Assignments

1. Let 0.1 be the probability that any given bit in a received word is incorrect. Compute the probability that a received word contains undetected errrors given the following coding schemes.
   1. No code, word length = 6
   2. even parity, word length = 6
2. What is the dimension of the binary vector space spanned by the set of vectors {(00101),(10100),(00110),(10001)}
3. Find a basis for the dual space to the binary vectors spanned by {(10011),(11100),(00111)}
4. Wicker, Chapter 4, Problem 1 (a),(b),(c),(d)
5. Wicker, Chapter 4, Problem 2 (a),(b),(c)
6. Wicker, Chapter 4, Problem 8 (a) also find a generator matrix for this code
7. Compute a syndrome decoding table for the code with parity check matrix
   |100011|
   |010101|
   |001110|
   

1. Wicker, Chapter 2, Problem 7
2. Express all of the nonzero elements of GF(13) as powers of a primitive element in GF(13)
3. Wicker, Chapter 2, Problem 30 (b), (d), (f)
4. Wicker, Chapter 2, Problem 34 (note GF(8) is given in Example 2-25)
5. Wicker, Chapter 4, Problem 14
6. Wicker, Chapter 4, Problem 15
7. Wicker, Chapter 4, Problem 16 (d), (f), (h)
8. Wicker, Chapter 4, Problem 20

1. Find lower and upper bounds on the required redundancy for a single error correcting code of length 15.
2. Wicker, Chapter 5, Problem 1
3. Wicker, Chapter 5, Problem 2
4. Wicker, Chapter 5, Problem 3
5. Wicker, Chapter 5, Problem 4 (a),(c)
6. Wicker, Chapter 5, Problem 5 (a),(c)
7. Wicker, Chapter 5, Problem 6 (a),(c)
8. Wicker, Chapter 5, Problem 7
9. Wicker, Chapter 5, Problem 8

1. Wicker, Chapter 3 Problem 11 (b),(d),(f)
2. Wicker, Chapter 3 Problem 12 (a),(b),(d)
3. Wicker, Chapter 3 Problem 13 (a),(e)
4. Wicker, Chapter 8 Problem 1
5. Wicker, Chapter 8 Problem 2
6. Wicker, Chapter 8 Problem 3
7. Wicker, Chapter 8 Problem 4 but use design distance 6
8. Wicker, Chapter 8 Problem 9 (a),(b)
9. Wicker, Chapter 9 Problem 2 (a),(c),(d)

Aaron Gulliver
2009-04-03