Due Monday, Dec 5th, 2022

For Monday:

  1. Please complete the FCQs for this course.  I really appreciate the time you take.  They are used for my own professional development, to inform decision-making in the department, and for promotion.
  2. Please also answer a few more specific questions about the course here for me:  here.  (This is an anonymous google form where you can help me understand how things like discord/daily posts etc. are helpful/not.)
  3. Consider the binary code C = {(0,0,1),(1,1,1),(1,0,0),(0,1,0)}.
      1. What is the length of C?
      2. What are the Hamming distances between the codewords (there are 6 pairs to check)?
      3. How many errors can C detect?
      4. How many errors can C correct?
      5. Suppose you send the codeword (1,1,1) and 2 errors are made on the noisy channel, in the first and last positions. Explain what message is received and what it decodes to. Was communication successful?
  4. In general, suppose a code has codewords which are all at Hamming distance d from each other (in other words, every pair is distance d).  How many errors can it detect?  How many errors can it correct?