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
