On Losev's method for fast vector-matrix multiplication

We propose an improvement of the algorithm of V. V. Losev [Radio Engrg. Electron. Phys. 25 (1980), no. 11, 116–119 (1982); MR0647612 (83f:94007)] which reduces the additive complexity of the multiplication of a binary $M\times M$ matrix (the elements of this matrix are $\pm1$) by a real vector, up to $M^2/\log_2M$ as $M\to\infty$.