Posted by: atri | April 27, 2012

## Clarification On Wednesday lecture

In class on Wednesday I had said that adding the extra power of $X$ to the definition of the original $E(X)$ would not preserve the original definition of an error location polynomial, i.e. $E(\alpha_i)=0$ if and only if there is an error at position $i$. However, for the proof of correctness of the Welch-Berlekamp algorithm we only need one direction, i.e. we need that if there is an error at location $i$, then $E(\alpha_i)=0$, which is satisfied by (12.3) in the book. You can verify that the proof of Claim 12.1.2 works as is.

Sorry for the confusion.