Math 422: Coding Theory

Midterm Exam

The midterm exam will take place on Thursday, February 28, during regular class time.

Notice this is a closed book exam. No sheets, no calculators, no books are allowed.

Amongn other things, you should be familiar with the definitions and theorems (and their meaning). More precisely, the following is a list of topics you should be very fluent in:

• definition of codes
• computations in finite fields (mainly mod p)
• minimum distance, nearest neighbour decoding, error detection and correction
• word error probability
• definition of A_q(n,d), some obvious values for A_q(n,d) (e.g. A_q(n,n) = q; also A₂(n,d) = A₂(n+1,d+1) if d is odd)
• Hamming distance, spheres in F_qⁿ, Hamming bound, perfect codes
• balanced block designs (and how to construct a code from one)
• linear codes
• minimum weight
• encoding with linear codes, standard array decoding, syndrome decoding
• generator and parity check matrices (def. and how to find them)
• dual code, Hamming Codes.

There will definitely be some proof questions on the exam.

The above list is not exhaustive.

You are not, for example, expected to know the Plotkin bound by heart. It is also not required to know all the proofs of theorems by heart (it is much more useful to understand them). On the other hand, a result like the Hamming bound/sphere packing bound would be something you are expected to be able to reproduce for yourself, should you forget the formula.

Here is last year's midterm exam and its solutions. There are also some sample questions and solutions. NB: the sample questions are not a sample midterm, but just a collection of problems for you to work on. Also be aware, that midterms vary over the years.
You may also find old midterms on Dr. Bowman's home page. Some of the problems there are from courses with a different schedule, though, so you may not be able to solve all problems.

It is a good idea to look at the old homework problems (including solutions) and solve sample problems, both from the sample exams and the book (or Dr. Bowman's Lecture Notes).

Finally, even though there are no regular office hours scheduled during Reading Week, if you have any questions about the material or homework or sample problems, please do not hesitate to write an e-mail or make an appointment!