Estimates of the Capacity of Orthogonal Arrays of Large Strength / Khalyavin A.V. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2010. № 3. P. 57-60 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 130-131].
D.G. Fon-Der-Flaass showed that Boolean correlation-immune n-variable functions of order m are resilient for m≥(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 (2n-2)/3, where n is a number of factors having size at least 2n-1 and all arrays of size 2n-1, are simple.
orthogonal array, boolean function, correlation-immune, lower bound.