We consider a list decoding algorithm recently proposed by Pellikaan-Wu
\cite{PW2005} for q-ary Reed-Muller codes RMqβ(β,m,n) of
length nβ€qm when ββ€q. A simple and easily accessible
correctness proof is given which shows that this algorithm achieves a relative
error-correction radius of Οβ€(1ββqmβ1/nβ). This is
an improvement over the proof using one-point Algebraic-Geometric codes given
in \cite{PW2005}. The described algorithm can be adapted to decode
Product-Reed-Solomon codes.
We then propose a new low complexity recursive algebraic decoding algorithm
for Reed-Muller and Product-Reed-Solomon codes. Our algorithm achieves a
relative error correction radius of Οβ€βi=1mβ(1βkiβ/qβ). This technique is then proved to outperform the Pellikaan-Wu
method in both complexity and error correction radius over a wide range of code
rates.Comment: 5 pages, 5 figures, to be presented at 2007 IEEE International
Symposium on Information Theory, Nice, France (ISIT 2007