| author: | Van H. Vu and Lei Wu |
|---|---|
| title: |
Improving the Gilbert-Varshamov 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 Gilbert-Varshamov 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)(q-1)
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
(q-1)/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
Gilbert-Varshamov 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.
285-288
|
| bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |
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| ps-source: | dmAE0156.ps (147 K) |
| pdf-source: | dmAE0156.pdf (146 K) |
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