2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Stefan Felsner (ed.)
DMTCS Conference Volume AE (2005), pp. 285288
author:  Van H. Vu and Lei Wu 

title: 
Improving the GilbertVarshamov bound for
q
ary codes

keywords:  
abstract: 
Given positive integers
q
,
n
and
d
, denote by
A
the maximum size of a
q
(n,d)
q
ary code of length
n
and minimum distance
d
. The famous GilbertVarshamov bound asserts that
A
where
q
(n,d+1) ≥q
n
/ V
q
(n,d),
V
is the volume of a
q
(n,d)=Σ
i=0
d
binom
(n, i)(q1)
i
q
ary sphere of radius
d
. Extending a recent work of Jiang and Vardy on
binary codes, we show that for any positive constant
α
less than
(q1)/q
there is a positive constant
c
such that for
d ≤αn
,
A
. This confirms a conjecture by Jiang and Vardy.
q
(n,d+1)≥cq
n
/ V
q
(n,d)n

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reference: 
Van H. Vu and Lei Wu (2005), Improving the
GilbertVarshamov bound for
q
ary codes, in 2005 European Conference on
Combinatorics, Graph Theory and Applications (EuroComb
'05), Stefan Felsner (ed.), Discrete Mathematics
and Theoretical Computer Science Proceedings AE, pp.
285288

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