\input zb-basic
\input zb-ioport
\iteman{io-port 05454045}
\itemau{Armand, Marc Andre}
\itemti{Improved list decoding of generalized Reed-Solomon and alternant codes over Galois rings.}
\itemso{IEEE Trans. Inf. Theory 51, No. 2, 728-733 (2005); correction 52, No. 11, 5167 (2006).}
\itemab
Summary: We present a two-stage list decoder comprising an errors-only Guruswami-Sudan (GS) decoder and an errors-and-erasures GS decoder as component decoders in the first and second stage, respectively. The two stages are coupled via a post-processor which selects a codeword from the output list of the first component decoder, from which erasure locations are obtained for the second stage. When applied to a generalized Reed-Solomon (RS) code over a Galois ring $R$ that maps into a generalized RS code of the same length $n$ and minimum (Hamming) distance $d$ over the corresponding residue field, the proposed decoder exploits the presence of zero divisors in $R$ to correct $s$ errors where $w=\lceil n-\sqrt{n(n-d)-1}\rceil