show/hide this revision's text 2 fixed typo

I'm a teaching assistant in an introductory course of Information Theory. I intend to prove the following well-known fact that easily proven using elementary information theoretic consideration: $\forall t\leq n/2 : \sum _{i=0} ^t \binom {n}{t} n}{i} \leq 2^{nH\left(\frac t n \right)}$

After this proof, I would like to present simple implications of it. So what I'm looking for is applications of this fact that yield non-trivial results. It is however important that the examples will require very little new definitions and as short introduction as possible. We assume that the students do have a standard undergraduate familiarity with Combinatorics, Graph Theory etc.
show/hide this revision's text 1

Simple uses for the Entropy bound on the volume of a Hamming ball

I'm a teaching assistant in an introductory course of Information Theory. I intend to prove the following well-known fact that easily proven using elementary information theoretic consideration: $\forall t\leq n/2 : \sum _{i=0} ^t \binom {n}{t} \leq 2^{nH\left(\frac t n \right)}$

After this proof, I would like to present simple implications of it. So what I'm looking for is applications of this fact that yield non-trivial results. It is however important that the examples will require very little new definitions and as short introduction as possible. We assume that the students do have a standard undergraduate familiarity with Combinatorics, Graph Theory etc.