Geodesic
On ranks of subsets in the space of binary vectors admitting an embedding of a Steiner system $S(2,4,v)$
Prikladnaâ diskretnaâ matematika, no. 1 (2014), pp. 73-76

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A bound for the rank of a subset $X$ in the vector space $\mathbb F_2^n$ is obtained via the covering radius of the code lying in the subspace of linear dependencies of vectors in $X$. Also, an upper bound for the covering radius of a code generated by the incidence matrix of a Steiner system $S(2,4,v)$ is obtained. Precice and asymptotic bounds for the rank of a subset $X$ in the vector space $\mathbb F_2^n$ admitting an embedding of a Steiner system $S(2,4,v)$ are obtained too.
Keywords: rank, affine rank, bounds, linear subspace, linear code, covering radius, Steiner system, Boolean functions, spectrum support. 
Y. V. Tarannikov. On ranks of subsets in the space of binary vectors admitting an embedding of a Steiner system $S(2,4,v)$. Prikladnaâ diskretnaâ matematika, no. 1 (2014), pp. 73-76. http://geodesic.mathdoc.fr/item/PDM_2014_1_a7/
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