  Recursive list decoding of Reed-Muller (RM) codes, with moderate list size,
is known to approach maximum-likelihood (ML) performance of short length $(\leq
256)$ RM codes. Recursive decoding employs the Plotkin construction to split
the original code into two shorter RM codes with different rates. In contrast
to the standard approach which decodes the lower-rate code first, the method in
this paper decodes the higher-rate code first. This modification enables an
efficient permutation-based decoding technique, with permutations being
selected on the fly from the automorphism group of the code using soft
information from a channel. Simulation results show that the error-rate
performance of the proposed algorithms, enhanced by a permutation selection
technique, is close to that of the automorphism-based recursive decoding
algorithm with similar complexity for short RM codes, while our decoders
perform better for longer RM codes. In particular, it is demonstrated that the
proposed algorithms achieve near-ML performance for short RM codes and for RM
codes of length $2^m$ and order $m - 3$ with reasonable complexity.
