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.

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