This article is cited in 3 papers

Coding Theory

An Improvement of Greismer Bound for Some Classes of Distances

S. M. Dodunekov, N. L. Manev


Abstract: Linear binary codes are considered. We prove that for $d=2^{k-2}-2^{а}-2^{Ь}$, $0\leq b<a\leq k-3$, $2\leq a$, $9\leq k$, the block length of a $k$-dimensional code with code distance $d$ is not less than
$$ 2+\sum_{j=0}^{k-1}\lceil\frac{d}{2^j}\rceil. $$


UDC: 621.391.1:519.725

 English version: Problems of Information Transmission, 1987, 23:1, 38–46

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