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Recursive constructions for equidistant permutation arrays

Part of: Designs and configurations

Published online by Cambridge University Press:  09 April 2009

P. J. Schellenberg  and
S. A. Vanstone
S. A. Vanstone
Affiliation:
University of Waterloo, Waterloo, Ontario
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Abstract

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An equidistant permutation array (EPA) is a ν × r array defined on an r-set, R, such that (i) each row is a permutation of the elements of R and (ii) any two distinct rows agree in λ positions (that is, the Hamming distance is (r−λ)).

Such an array is said to have order ν. In this paper we give several recursive constructions for EPA's.

The first construction uses a resolvable regular pairwise balanced design of order v to construct an EPA of order ν. The second construction is a generalization of the direct product construction for Room squares.

We also give a construction for intersection permutation arrays, which arrays are a generalization of EPA's.

MSC classification

Secondary: 05B30: Other designs, configurations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 24 , Issue 2 , September 1977 , pp. 216 - 223
Copyright
Copyright © Australian Mathematical Society 1977

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