  In the present note, we study a new method of constructing efficient
coverings for Kronecker powers of matrices, recently proposed by J. Alman, Y.
Guan, A. Padaki [arXiv, 2022]. We provide an alternative proof for the case of
symmetric matrices in a stronger form. As a consequence, the previously known
upper bound on the depth-2 additive complexity of the boolean $N\times N$
Kneser-Sierpinski matrices is improved to $O(N^{1.251})$.
