Asymptotic Improvement of the Gilbert–Varshamov Bound for Linear Codes
- 26 August 2008
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Information Theory
- Vol. 54 (9), 3865-3872
- https://doi.org/10.1109/tit.2008.928288
Abstract
The Gilbert-Varshamov (GV) bound states that the maximum size A2(n, d) of a binary code of length n and minimum distance d satisfies A2(n, d)ges2n/V(n, d-1) where V(n, d)=Sigmai=0 d(i n) stands for the volume of a Hamming ball of radius d. Recently, Jiang and Vardy showed that for binary nonlinear codes this bound can be improved to A2(n, d)gescn2n/(V(n, d-1)) for c a constant and d/nges0.499. In this paper, we show that certain asymptotic families of linear binary [n, n/2] random double circulant codes satisfy the same improved GV bound.Keywords
This publication has 10 references indexed in Scilit:
- On the construction of dense lattices with a given automorphisms groupAnnales de l'institut Fourier, 2007
- Asymptotic improvement of the Gilbert-Varshamov bound for binary linear codesPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2006
- Improving the Gilbert–Varshamov Bound for$q$-Ary CodesIEEE Transactions on Information Theory, 2005
- Asymptotic Improvement of the Gilbert–Varshamov Bound on the Size of Binary CodesIEEE Transactions on Information Theory, 2004
- Modular curves, Shimura curves, and Goppa codes, better than Varshamov‐Gilbert boundMathematische Nachrichten, 1982
- A Gilbert-Varshamov bound for quasi-cycle codes of rate 1/2 (Corresp.)IEEE Transactions on Information Theory, 1974
- Some results on quasi-cyclic codesInformation and Control, 1969
- New binary coding results by circulantsIEEE Transactions on Information Theory, 1969
- Low-Density Parity-Check CodesPublished by MIT Press ,1963
- A Comparison of Signalling AlphabetsBell System Technical Journal, 1952