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Association Schemes for Ordered Orthogonal Arrays and (T, M, S)-Nets

Published online by Cambridge University Press:  20 November 2018

W. J. Martin  and
D. R. Stinson
W. J. Martin
Affiliation:
Mathematics and Statistics, University of Winnipeg, Winnipeg, Manitoba R3B 2E9 email: William.Martin@UWinnipeg.ca
D. R. Stinson
Affiliation:
Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, N2L 3G1 email: dstinson@cacr.math.uwaterloo.ca
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Abstract

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In an earlier paper [10], we studied a generalized Rao bound for ordered orthogonal arrays and $(T,\,M,\,S)$-nets. In this paper, we extend this to a coding-theoretic approach to ordered orthogonal arrays. Using a certain association scheme, we prove a MacWilliams-type theorem for linear ordered orthogonal arrays and linear ordered codes as well as a linear programming bound for the general case. We include some tables which compare this bound against two previously known bounds for ordered orthogonal arrays. Finally we show that, for even strength, the $\text{LP}$ bound is always at least as strong as the generalized Rao bound.

Keywords

05B1505E3065C99
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 51 , Issue 2 , 01 April 1999 , pp. 326 - 346
Copyright
Copyright © Canadian Mathematical Society 1999

References

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