Spielman showed that one can construct error-correcting codes capable
of correcting a constant fraction $\delta << 1/2$ of errors,
and that are encodable/decodable in linear time.
Guruswami and Sudan showed that it is possible to correct
more than $50\%$ of errors (and thus exceed the ``half of the minimum
distance barrier''), with polynomial-time encoding and decoding.
In this paper we show that it is possible to achieve these two properties
*simultanously*. Specifically, we give a construction of constant rate,
linear-time encodable codes that are capable of correcting any $\delta<2/3$
fraction of errors in linear time.
Our codes are constructed using high-quality expander graphs.