Summary: On the Average List Size for the Guruswami-Sudan Decoder
R. J. McEliece
California Institute of Technology
Abstract: In this paper we will show that the (hard-
decision) Guruswami-Sudan Reed-Solomon 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