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.

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.)

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?