Math3152 Coding Theory Exam FAQ 2008

FAQ

• Q: What was that list of hot revision topics again?
  A: They include: Cartesian product; Hamming distance; triangle inequality; minimum distance; ball-packing bound; p(error); code parameters; finite fields and spaces; linear codes; dual codes; standard array; syndrome decoding; along with some other things we have discussed.
• Q: Will we be given solutions for some of the past exams?
  A: Good question. I don't have access to the original model solutions. However there are good model solutions to a past mock exam (that is highly representative of our paper) available from the webpage.
  I will also work through some of the most interesting questions from 2005 and 2006 in class under 'exam' conditions. This will be an exciting test for me (!), but should also result in me producing good solutions in class, which you can of course copy down.
• Q: Will we need to know for the exam the proofs that you asked us to prove ourselves, or will we just be examined on those proofs that are in the notes?
  A: Good question. In addition to the ones we did in class, some of the ones I left for you to do as exercises might come up. (But before you start worrying - it would only be relatively easy ones. I'll give some verbal indications in class.)
  You should also be prepared to answer questions of the form which require you to prove the non-existence of a code with certain given parameters (see Exercise sheets for examples).
  And of course there are a small number of question parts in the exam inviting you to demonstrate your mastery of the material by going _beyond_ what we have seen.
• Q: Can we have a list of proofs that we might be expected to reproduce in the exam?
  A: I will give some verbal indications. (Also see answer above.)
• Q: What are the right answers for Problems 2 Q1?!
  A: (a) 2x2x2x2=1, and 3x3x3x3=1, so 1+3=4 (mod.5)
  (b) 1x3=3
  (c) 1-3=3
  (d) 1/3=2
• Q: I think there might be a typo in the notes (for example in the statement of the theorem relating the dimension of a code to the dimension of the dual code). Is that possible?
  A: Yes it is very possible. Producing a book of notes like this is a big task, and they never seem to come out perfect. The hope is that enough of it is right that you can at least spot the inconsistencies and see how to fix them.
  (In the case you mention, I confirm that the dual code is a [n,n-k]-code, not a [n-k,k]-code as the typo in the notes suggests. Of course both the code and the dual come from the space of codewords of the same length (n), so it must be [n,something]!)
• Q: It's all too hard/easy for me. Can you slow down/speed up?
  A: Sure, within certain limits. Our speed is dictated by the material in the module, which we cover, and by the fact that the more carefully we go, the deeper our understanding can be. (I appreciate that deep understanding and passing an exam are not quite the same, but the former is important.) Since we have succeeded in covering the material of the module now, if you want to do more (and faster?) you need to propose some specific revision questions that you feel you are weak on. Then we can work (quickly, if need be) through these.

Past examination papers

• 2003
• 2005
• 2006
  Selected answers:
  • 1(a)(iii) d=5
  • 1(b)(ii) Have bound on M from BP. But also for a linear 3-ary code M=3^k. So an upper bound on k is given by the largest k so that 3^k does not exceed the BP bound.
  • (iii) use the k above.