Talk:Linear code

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[edit] Notation for Linear vs Non-Linear codes

The article uses the notation "(n, k, d)-code" to refer to a linear code of length n, rank k, and minimum distance d; and uses "[n, r, d]-code" to refer to a non-linear code of length n, r codewords, and minimum distance d. I'm not trying to be controversial, but was this done on purpose? Is this the notation used by "Elements of Information Theory" (the listed reference)? (Unfortunately, my local library's copy of "Elements of Information Theory" is currently checked out, so I cannot verify whether it uses this notation.)

I bring this up because in my Coding Theory class two different professors and our textbook ("A First Course in Coding Theory", by Raymond Hill) use the exact opposite notation: namely, "(n, k, d)-code" to refer to any code, and "[n, r, d]-code" to specify a linear code. This difference could be quite confusing if Wikipedia articles do not follow a consistent format, so I wanted to ask before I write anything. Is there a notation standard among mathematicians or coding theorists? --Culix (talk) 05:34, 26 February 2008 (UTC)

I had the same question upon first encountering this article. I've always seen the opposition notation. I skimmed the current reference on Amazon and couldn't find either notation. Although I note this reference was added much later than the notation and so probably isn't the source for that. Some other books I randomly flipped through (Introduction to Coding and Information Theory by Roman, Coding Theory: A First Course by Ling and Xing, and Sphere Packings, Lattices, and Groups by Conway and Sloane) all use the notation you mention. Perhaps the article is in error. -- Fropuff (talk) 07:31, 26 February 2008 (UTC)
I used the notation based on what I had learned in my university course. However they don't seem to use that notation any more. The recommended books for the course are the following. You might like to check the notation used in them if it worries you. I wouldn't bother: I don't see why wikipedia can't just define its own notation and then use it consistently. That is to say, go ahead and feel free to introduce a new notation. reetep (talk) 12:17, 29 February 2008 (UTC)
  • G.M. Goldie & R.G.E. Pinch, Communication Theory, Cambridge University Press 1991.
  • D. Welsh Codes and Cryptography, Oxford University Press 1988.
  • T.M. Cover & J.A. Thomas Elements of Information Theory, Wiley 1991.
  • W. Trappe & L.C. Washington Introduction to Cryptography with Coding Theory, Prentice Hall, 2002.
  • J.A. Buchmann, Introduction to Cryptography, (2nd Ed.), Springer UTM, 2004
Should it be of interest, you can see the notation in use in a legacy set of notes from Cambridge University. reetep (talk) 21:48, 2 March 2008 (UTC)
My Coding Theory professor said he was not aware of any international notation standard either. This is unfortunate, but I suppose as long as we're consistent you're right; we could pick whatever format we wanted. I'd be fine with using '[n,k,d]-code' for regular codes and '(n,k)-code' for linear codes if everyone thought it was better. For now I'll stick with '(n,k,d)-code' for regular codes and '[n,k]-code' for linear codes.
Where would we document this sort of thing? On the main coding theory article? On the [Coding Theory Category page]? --Culix (talk) 22:33, 12 March 2008 (UTC)