Multistage list decoding of generalized Reed-Solomon codes over Galois rings

A two-stage list decoder for generalized Reed-Solomon codes over GR (p^l,m) that can exceed the Guruswami-Sudan decoding radius t_GS with significant probability for p=2, l≥2 and m=1 was recently proposed. It makes a distinction between error values which are units and those which are zero divisors in order to exceed t_GS. This letter presents an extension of that approach by exploiting the fact that each element of GR (p^l,m) has a unique p-adic expansion, culminating in a multistage decoder that outperforms the two-stage decoder.