# Counting the number of codes

1. Aug 1, 2012

### chiaroscuro

Hi all.

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

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

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

Any help would be much appreciated. Thanks!