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Counting the number of codes

  1. Aug 1, 2012 #1
    Hi all.

    Let [itex]C[/itex] and [itex]D[/itex] be codes of length n over [itex]\mathbb{F}_q[/itex] of dimension [itex]k[/itex] and [itex]k+l[/itex] respectively.

    I want to count the number of codes [itex]D[/itex] such that [itex]C\subseteq D\subseteq (C^\perp\cap D^\perp)[/itex].

    I understand that this will involve the Gaussian coefficient. If I'm not mistaken, I think it would be of the form [itex]{A\choose l }_q[/itex] but I can't figure out what [itex]A[/itex] is.

    Any help would be much appreciated. Thanks!
     
  2. jcsd
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