%0 Journal Article
%@ 0925-1022
%A  Carlet Claude
%A  Kiss Rebeka
%A  Nagy Gábor Péter
%A Algebra Tanszék BME / TTK / MI AT [2000-2023],
%D 2023
%F publicatio:29112
%J DESIGNS CODES AND CRYPTOGRAPHY
%N 1
%P 151-163
%T Simplicity conditions for binary orthogonal arrays
%U http://publicatio.bibl.u-szeged.hu/29112/
%V 91
%X It is known that correlation-immune (CI) Boolean functions used in the framework of side channel attacks need to have low Hamming weights. The supports of CI functions are (equivalently) simple orthogonal arrays, when their elements are written as rows of an array. The minimum Hamming weight of a CI function is then the same as the minimum number of rows in a simple orthogonal array. In this paper, we use Rao's Bound to give a sufficient condition on the number of rows, for a binary orthogonal array (OA) to be simple. We apply this result for determining the minimum number of rows in all simple binary orthogonal arrays of strengths 2 and 3; we show that this minimum is the same in such case as for all OA, and we extend this observation to some OA of strengths 4 and 5. This allows us to reply positively, in the case of strengths 2 and 3, to a question raised by the first author and X. Chen on the monotonicity of the minimum Hamming weight of 2-CI Boolean functions, and to partially reply positively to the same question in the case of strengths 4 and 5.
%Z Funding Agency and Grant Number: Budapest University of Technology and Economics             Funding text: Open access funding provided by Budapest University of Technology and Economics.