Separable Codes for the Symmetric Multiple-Access Channel

A binary matrix is called an
${s}$
-
separable code
for the
disjunctive multiple-access channel
(
disj-MAC
) if Boolean sums of sets of
${s}$
columns are all distinct. The well-known issue of the combinatorial coding theory is to obtain upper and lower bounds on the rate of
${s}$
-separable codes for the
${disj}$
-MAC. In our paper, we generalize the problem and discuss upper and lower bounds on the rate of
${q}$
-ary
${s}$
-separable codes for the models of noiseless
symmetric
MAC, i.e., at each time instant the output signal of MAC is a symmetric function of its
${s}$
input signals.