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Estimates of the capacity of orthogonal arrays of large strength

A. V. Khalyavin

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: D. G. Fon-Der-Flaass showed that Boolean correlation-immune $n$-variable functions of order $m$ are resilient for $m\ge\frac{2n-2}{3}$. In this paper this theorem is generalized to orthogonal arrays. It is shown that orthogonal arrays of strength $m$ not less than $\frac{2n-2}{3}$, where $n$ is a number of factors having size at least $2^{n-1}$ and all arrays of size $2^{n-1}$ are simple.

Key words: orthogonal array, boolean function, correlation-immune, lower bound.

UDC: 519.142

Received: 14.12.2009

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