Due Monday, November 30th

For Mon:

• I hope everyone has/had a wonderful thanksgiving, whether remote, take-out, whatever it is/was.  🙂
• I’ve opened a “Re-Do Module 3 and 4” assignment on canvas.  It will work like the Re-Do for Module 1 and 2.  In other words, you can do a replacement problem for problems on the assessments, for up to 80% replacement credit.  Please email me to request that I add problems to it, and I will keep adding them as needed.  This will be due the last day of class (December 7th), so make requests by December 4th at latest (note: solutions and grading for Mod 4 will happen this weekend).
• To Do:
• Compute the continued fraction of 31/64 by hand.
• 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?
• 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?