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)}.

What is the length of C?

What are the Hamming distances between the codewords (there are 6 pairs to check)?

How many errors can C detect?

How many errors can C correct?

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?