Asymptotic improvement of the Gilbert-Varshamov bound for linear codes

Details Asymptotic improvement of the Gilbert-Varshamov bound for linear codes Asymptotic improvement of the Gilbert-Varshamov bound for linear codes

2007-08-30

arxiv.org/abs/0708.4164v1

IEEE Transactions on Information Theory, IT-54, No. 9 (2008) pp. 3865--3872.

Computer Science

Information Theory

Submitted to IEEE Transactions on Information Theory

Scientific paper

10.1109/TIT.2008.928288

The Gilbert-Varshamov bound states that the maximum size A_2(n,d) of a binary code of length n and minimum distance d satisfies A_2(n,d) >= 2^n/V(n,d-1) where V(n,d) stands for the volume of a Hamming ball of radius d. Recently Jiang and Vardy showed that for binary non-linear codes this bound can be improved to A_2(n,d) >= cn2^n/V(n,d-1) for c a constant and d/n <= 0.499. In this paper we show that certain asymptotic families of linear binary [n,n/2] random double circulant codes satisfy the same improved Gilbert-Varshamov bound.

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