We show how to extend the \emph{bivariate} interpolation decoding
algorithm of Guruswami--Sudan to multivariate interpolation
decoders by decoding $M$ Reed-Solomon codewords together.
When the errors are \emph{synchronized} - occurs at the same
position for all $M$ codewords - the proposed decoding algorithm
can decode up to $1 - R^{M/(M+1)}$ fraction of errors efficiently
with high probability over a $q$-ary symmetric channel, where $R$
is rate of the code.

We also present new algebraic codes for the \emph{adversarial} channel.
We prove that up to a $1 - \sqrt[M+1]{(MR)^M}$
fraction of errors can be efficiently list decoded when we are transmitting
a \emph{subset} of Reed-Solomon codes, chosen in a clever way. This beats the
decoding bound of Guruswami--Sudan for rates smaller that $1/16$.
