Minimal 2-coverings of a finite affine space based on GF(2)

TitleMinimal 2-coverings of a finite affine space based on GF(2)
Publication TypeJournal Article
AuthorsKatona, G. O. H., and J. Srivastava
Journal titleJournal of Statistical Planning and Inference
Year1983
Pages375 - 388
Volume8
Abstract

Let EG(m, 2) denote the m-dimensional finite Euclidean space (or geometry) based on GF(2), the finite field with elements 0 and 1. Let T be a set of points in this space, then T is said to form a q-covering (where q is an integer satisfying 1less-than-or-equals, slantqless-than-or-equals, slantm) of EG(m, 2) if and only if T has a nonempty intersection with every (m-q)-flat of EG(m, 2). This problem first arose in the statistical context of factorial search designs where it is known to have very important and wide ranging applications. Evidently, it is also useful to study this from the purely combinatorial point of view. In this paper, certain fundamental studies have been made for the case when q=2. Let N denote the size of the set T. Given N, we study the maximal value of m.

Languageeng
Notes

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