Orthogonal systems View Full Text


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Article Info

DATE

1978-02

AUTHORS

M. Deza, R. C. Mullin, S. A. Vanstone

ABSTRACT

An equidistant permutation array (E.P.A.)A(r, λ v) is av × r array in which every row is a permutation of the integers 1, 2, ⋯,r such that any two distinct rows have precisely λ columns in common. In this paper we introduce the concept of orthogonality for E.P.A.s. A special case of this is the well known idea of a set of pairwise orthogonal latin squares. We show that a set of these arrays is equivalent to a particular type of resolvable (r, λ)-design. It is also shown that the cardinality of such a set is bounded byr − λ with the upper bound being obtained only ifλ = 0. A brief survey of related orthogonal systems is included. In particular, sets of pairwise orthogonal symmetric latin squares, sets of orthogonal Steiner systems and sets of orthogonal skeins. More... »

PAGES

322-330

References to SciGraph publications

  • 1970-06. Orthogonal steiner systems in AEQUATIONES MATHEMATICAE
  • 1976-10. The construction of orthogonalk-skeins and latink-cubes in AEQUATIONES MATHEMATICAE
  • 1975-02. The existence of Room squares in AEQUATIONES MATHEMATICAE
  • 1973-06. Construction of perpendicular steiner quasigroups in AEQUATIONES MATHEMATICAE
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    http://scigraph.springernature.com/pub.10.1007/bf01818570

    DOI

    http://dx.doi.org/10.1007/bf01818570

    DIMENSIONS

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