Improvement of the Code-Length Lower Bound for a Multiple-Access Adder Channel

In [1: A. G. D'yachkov and V. V. Rykov, Probl. Peredachi Inf., 1981, vol. 17, no. 2, pp. 26–38], the notion of a $B_s$-code was introduced for some coding problems for a multiple-access adder channel. These problems are related to conflict resolution in RMA systems [B. S. Tsybakov and V. A. Mikhailov, Probl. Peredachi Inf., 1978, vol. 14, no. 4, pp. 32–59; A. G. D'yachkov and V. V. Rykov, Proc. 6th All-Union Workshop on Comm. Networks, Part 4, Moscow, 1981, pp. 18–24]. In [1], upper and lower bounds for the length of optimum $B_s$-codes were obtained. In the present paper, we improve the lower bound from [1] for the case of odd $s$.