 
Summary: On the Average List Size for the GuruswamiSudan Decoder
R. J. McEliece
California Institute of Technology
rjm@systems.caltech.edu
Abstract: In this paper we will show that the (hard
decision) GuruswamiSudan ReedSolomon list de
coder almost always returns a list of size one, and
therefore is in fact not really a list decoder at all.
We will do this by giving exact formulas for, and
simplified approximations to, the expected number
of RS codewords in a sphere of radius t centered at
a randomly chosen word of weight u, which is the
same as the expected number of noncausal code
words in the GSD list, conditioned on the error pat
tern having weight u.
1. Introduction. List Decoding in General.
If C is an (n, k) linear code, a conventional decoder
for C maps each possible received sequence into a
unique codeword, and is in error if the offered code
word is not the transmitted one. A list decoder [4]
