Boolean designs and self-dual matroids

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12 Scopus citations

Abstract

In this paper we consider a variety of questions in the context of Boolean designs. For example, Erdös asked: How many subsets of an n-set can be found so that pairwise their intersections are all even (odd)? E. Berlekamp [2] and the author both answered this question; the answer is approximately 2[ 1 2n]. Another question which can be formulated in terms of Boolean designs was asked by J. A. Bondy and D. J. A. Welsh [1]. For what values of d can one find a connected binary matroid of rank d which is identically self-dual? We prove that such matroids exist for all d except 2, 3, and 5. The paper ends with a discussion of more general modular designs and with constructions of some identically self-dual matroids representable over the field of three elements.

Original languageEnglish (US)
Pages (from-to)111-128
Number of pages18
JournalLinear Algebra and Its Applications
Volume10
Issue number2
DOIs
StatePublished - Apr 1975

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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