Coding Theory - Homework #1

Problems from the text: pg. 14: 4, 5, 6, 7
and the following questions:
  1. If the 6th digit of this ISBN is unreadable, determine it assuming that all the other digits are correct. ISBN 0 - 13 - 06x464 - 8.
  2. Determine the U.S. Post Office Delivery Point Code for your home address.
  3. Compare the probability of error for the 4-repeat code and the 5-repeat code.
  4. Determine the code rate for the Hamming example of a 1-error correcting code given in class.
  5. Compare the code rates of the 3-repeat code (which is 1-error correcting) with that of the Hamming example above.
  6. Show that the error-correcting capability of the Hamming example is not reduced if the last digit [the (t+1)2 -st digit] is dropped from the codewords.