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Recursive decoding techniques are considered for Reed-Muller (RM) codes ofgrowing length $n$ and fixed order $r.$ An algorithm is designed that hascomplexity of order $n\log n$ and corrects most error patterns of weight up to$n(1/2-\varepsilon)$ given that $\varepsilon$ exceeds $n^{-1/2^{r}}.$ Thisimproves the asymptotic bounds known for decoding RM codes with nonexponentialcomplexity.

Recursive Decoding and Its Performance for Low-Rate Reed-Muller Codes