I'm looking for error-correcting codes of the following type:
binary codes with constant rate,
decodable from some constant fraction of errors, by a decoder implementable as a Boolean circuit of size $O(N)$, where $N$ is the encoding length.
Spielman, in Linear-Time Encodable and Decodable Error-Correcting Codes, gave codes decodable in $O(N)$ time in the logarithmic-cost RAM model, and also decodable by $O(N \log N)$-sized circuits.
Guruswami and Indyk gave an improved construction in Linear Time Encodable/Decodable Codes with Near-Optimal Rate. They don't analyze the resulting circuit complexity, although I believe it is also $\Theta(N \log N)$.
Thanks in advance!