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Bounds on orthogonal arrays and resilient functions

✍ Scribed by Jürgen Bierbrauer

Publisher
John Wiley and Sons
Year
1995
Tongue
English
Weight
212 KB
Volume
3
Category
Article
ISSN
1063-8539

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✦ Synopsis

The only known general bounds on the parameters of orthogonal arrays are those given by Rao in 1947 [J. Roy. Statist. Soc. 9 (1947), 128-1391 for general O A ~ ( t , k , v ) and by Bush [Ann. Math. Stat. 23, (1952), 426-4341 [3] in 1952 for the special case A = 1. We present an algebraic method based on characters of homocyclic groups which yields the Rao bounds, the Bush bound in case t 2 v, and more importantly a new explicit bound which for large values of t (the strength of the array) is much better than the Rao bound. In the case of binary orthogonal arrays where all rows are distinct this bound was previously proved by Friedman [Proc. 33rd IEEE Symp. on Foundations of Comput. Sci., (1992), 314-3191 in a different setting. w e also note an application to resilient functions. 0 1995 John Wiley & Sons, he.

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