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Asymptotic Improvement of the Gilbert–Varshamov Bound for Linear Codes

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2 Author(s)
Gaborit, P. ; XLIM, Univ. de Limoges, Limoges ; Zemor, G.

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.

Published in:

Information Theory, IEEE Transactions on  (Volume:54 ,  Issue: 9 )