Posted by: atri | February 11, 2011

## Lecture 10: Volume of a Hamming Ball

In today’s lecture we proved upper and lower bounds on the volume of a Hamming ball in terms of the $q$-ary Entropy function. Then we saw the $R$ vs. $\delta$ tradeoff given by the Hamming bound and the GV bound.

Today’s material is from Lecture 9 and 15 from Fall 2007.

Next lecture, we will complete the proof of the Gilbert construction and then move to the Varshamov construction. The latter uses probability. You might want to glance through Lecture 4 from Spring 2009 for a probability primer.