Graphs and Combinatorics

, Volume 3, Issue 1, pp 81–89 | Cite as

On schematic orthogonal arraysOA(q t ,k, q, t)

  • Mitsuo Yoshizawa
Article

Abstract

Am × k matrixA, with entries from a set ofq ≧ 2 elements, is called an orthogonal arrayOA(m, k, q, t) (t ≧ 2) if eachm × t submatrix ofA contains all possible 1 ×t row vectors with the same frequencyλ(m = λq t ). We call the array schematic if the set of rows ofA forms an association scheme with the relations determined by the Hamming distance. In this paper we determine the schematic orthogonal arraysOA(q t ,k, q, t) with2t − 1 > k.

Keywords

Association Scheme 

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References

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    Atsumi, T.: A study of orthogonal arrays from the point of view of design theory. J. Comb. Theory (A)35, 241–251 (1983)Google Scholar
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    Bose, R.C., Mesner, D.M.: On linear associative algebras corresponding to association schemes of partially balanced designs. Ann. Math. Statist.30, 21–38 (1959)Google Scholar
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    Delsarte, P.: An algebraic approach to the association schemes of coding theory. Philips J. Res. Rep. Suppl.10 (1973)Google Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Mitsuo Yoshizawa
    • 1
  1. 1.Department of MathematicsJosai UniversityKeyakidai, SakadoJapan

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