Math3152/5153 Coding Theory Exam FAQ 2018

FAQ (Mainly a summary of FAQs and answers from our lectures)

• Q: What was that list of hot revision topics for 3153 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 the past exams?
  A: Good question. I don't have access to the original indicative solutions in all cases. However there are good indicative solutions to a past exam (that is highly representative of our paper) available from the webpage.
  I will also work through some of the most interesting questions from 2015 and 2016 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: I am hoping and aiming for a nice solid first class mark, nothing more. Do I need to read the answer to the question after this one?
  A: Perhaps only if you are curious. ;-)
• Q: I am a super-smart student aiming for a super-high grade. What extra work should I do?
  A: Interesting question. We tend to think of the super-high grades (85+ perhaps) as reserved for attempts so good that the student is a potential candidate for a PhD later. (Is that you?)
  If so, then you should keep in mind that such people are held to a higher standard of mathematical writing - more like a professional mathematician writing to inform a client than a kid hoping to convince the teacher that they know something - if they are going to get those last couple of extra marks. (If that makes sense!?) So,...
  ALWAYS (ALWAYS) write in sentences.
  To get those last couple of top marks, your proofs must read like logical arguments.
  If you look at the indicative answers to past exams, keep in mind that `proof' is a relative activity (i.e. how much to write depends on who you are writing for). In preparing indicative answers the author might write just enough to help you see your way through a proof. This would include indications of the key points for which marks can be given. But it might just possibly jump over some of the actual arguments, in cases where they are straightforward. In answering in an exam, you probably need to be more careful, more thorough, than this. And of course you need to _give_ those arguments explicitly.
  Actual maths is an act of communication. So try to make sure you are writing in a way that communicates. (In an exam there is not much time. It won't be perfect. But for the very top marks, this is what we are looking for.)
  Do _not_ claim you have proved something when you have not.
• Q: Can I invent my own notation in the exam and use it without explaining it?
  A: No.
• Q: My writing is scruffy. Is that a problem?
  Scruffy? Not a problem. Illegible? Yes, a problem. Find a way to fix it.
  Again, maths is partly an act of communication (of truth). You could fail to do that by communicating something that is not truth; or by being illegible.
  In Coding Theory, which is literally about communicating accurately, it would be highly ironic to fail to do this by making your own handwriting a very noisy channel!!
• 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.