Posted by: atri | February 10, 2010

## Lecture 12: Bounds on the Volume of a Hamming Ball

In today’s lecture we proved tight upper and lower bounds on the volume of a Hamming ball. (This material is from Lecture 9 (Sec 1.2) from Fall 07.) Using these bounds we saw that fractional version of the Hamming bound satisfies

$R\le 1-H_q\left(\frac{\delta}2\right)+o(1)$.

We then saw the GV bound

$R\ge 1-H_q(\delta)-\epsilon$.

We began with the greedy construction due to Gilbert. (This material is in Lecture 15 from Fall 07).