Hi all.(adsbygoogle = window.adsbygoogle || []).push({});

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!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Counting the number of codes

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**