We have a lot of administrivia with the end of semester approaching! Please read carefully through all this to maximize your grade!
This week is the last week for in-person make-ups. Reminder: you can make up at most one problem per test for Tests 1-3. If you scored 6 or less on your chosen problem, use my appointments calendar link (on canvas or discord) to make a 15 minute appointment for the problem. If you scored 7 or higher, you can do a written make-up due last day of class; you can see the makeup problems and dropbox in canvas. [editor’s note: canvas setup still in progress]
I’ve made a poster page to show off all the beautiful posters you made! Check it out here. You should consider presenting these at Math For All in April!
On the discord I posted a link to the poster presentation order for Fri Dec 6 / Monday 9th. Please be on time, since I’m going to have a timer set up to manage the slots and we are sticking to the schedule!
On Wednesday, Dec 11th, class will be a pre-recorded lecture which you can view at your leisure (I’m travelling).
Please review your self-eval sheets for daily posts and make sure they are nearly ready for final submit on the last day of class (on canvas upload).
Please be aware the final exam is cumulative, and includes coding theory.
FCQs are open! These matter! Please fill it out with your honest opinions and suggestions, as I try to improve the course each year. Here’s the link.
I won’t be able to have in-person review session for final (because of my travel) but I will try to make up for it by responding to discord requests with short video explanations of problems.
For those doing extra time, make sure you have arranged your final exam with me.
If needed, you’ll want to review the following aspects of linear algebra for studying linear codes:
vectors and matrix multiplication
vector space and subspace
span
basis (independence, uniqueness of expression in terms of a basis)
dimension
kernel of a linear transformation
row-space and column-space
rank-nullity theorem
transpose of a matrix
Consider the binary code C = {(0,0,1),(1,1,1),(1,0,0),(0,1,0)}. The alphabet is {0,1}.
What is the length of C?
What is d(C) (the minimum distance)?
What are q, n, M and d if C is a q-ary (n,M,d)-code?
How many errors can C detect?
How many errors can C correct?
Show that C is not linear.
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 via nearest neighbour decoding. Was communication successful?
Show that C is a coset of a linear code. (The definition of a coset is a translation, by some vector, of a subspace). What is the linear code? Call it C’.