Back to Search
Start Over
Improving the Gilbert--Varshamov Bound for q-Ary Codes.
- Source :
- IEEE Transactions on Information Theory; Sep2005, Vol. 51 Issue 9, p3200-3208, 9p
- Publication Year :
- 2005
-
Abstract
- Given positive integers q, n, and d, denote by A<subscript>q</subscript>(n,d) the maximum size of a q-ary code of length vi and minimum distance d. The famous Gilbert-Varshamov bound asserts that A<subscript>q</subscript>(n,d+1) ≥ q<superscript>n</superscript>/V<subscript>q</subscript>(n,d) where is the volume of a 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. This confirms a conjecture by Jiang and Vardy. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 51
- Issue :
- 9
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 18086386
- Full Text :
- https://doi.org/10.1109/TIT.2005.853300