Posted by: atri | October 10, 2007

## Lecture 19: Elias-Bassalygo Bound

Today we proved the Elias-Bassylygo bound between rate $R$ and relative distance $\delta$ of a $q$-ary code: $R\le 1-H_q(J_q(\delta))+o(1)$, where $J_q(\delta)=\left(1-\frac{1}{q}\right)\left(1-\sqrt{1-\frac{q\delta}{q-1}}\right)$.

We also looked at secret sharing and saw some “trivial” schemes. Next lecture, we will look at some more interesting schemes that are based on codes.