Dual fail-safe separating systems (Q1103588)

This paper deals with the following coding problem: Let C, D be codes. The pair (C,D) is called a dual (2,2)-separating system with \(\eta\)- separation if for all c \(1\neq c\) \(2\in C\) and for all d \(1\neq d\) \(2\in D\), \(\# (i: c\quad 1_ i=d\quad 1_ i\neq c^ 2_ i=d^ 2_ i)=\eta.\) Given \(M_ 1=| C|\) and n, maximize \(M_ 2=| D|\). - The problem is connected with fault tolerant encoding of discrete automata states. The author gives asymptotic (n\(\to \infty)\) upper and lower bounds for \(R_ 2\) in terms of \(R_ 1\) and \(\delta\), where \(R_ 1=(\) 2log \(M_ 1)/n\), \(R_ 2=(\) 2log \(M_ 2)/n\), \(\delta =\eta /n\). In Definition 1 for inadequate pairs the word ``no'' is left out. It should be: A pair of vectors is called inadequate... if ``no'' \(\eta\) coordinates.... In the proof of the lower bound there are a few details which are not quite clear but I guess that the proof can be repaired easily. Unfortunately the lower bound is not constructive, so there remains an interesting task in constructing (2,2)-separating systems.