On implementation of some systems of elementary conjunctions in the class of separating contact circuits

We show that the system of elementary conjunctions $\Omega_{n,2^k} = {K_0,\ldots,K_{2^{k} -1}}$ such that each conjunction depends essentially on $n$ variables and corresponds to some codeword of a linear $(n, k)$-code can be implemented by a separating contact circuit of complexity at most $2^{k+1} + 4k(n - k) - 2$. We also show that if a contact $(1, 2^k)$-terminal network is separating and implements the system of elementary conjunctions $\Omega_{n,2^k}$, then the number of contacts in it is at least $2^{k+1} - 2$.