With the Delsarte-MacWilliams inequalities as a starting point, an upper bound is obtained on the rate of a binary code as a function of its minimum distance. This upper bound is asymptotically less than Levenshtein's bound, and so also Elias's.

An upper bound on the minimum distance of binary blocks codes, which is superior to Elias' bound for R < 0.0509^+, is obtained. The new bound has the same derivative(-infty) at R = 0 as Gilbert's lower bound. (Elias' bound has derivative-ln 2 at R = 0).

Given a finite probability spaceXand an a priori distributionP = P(0) = \{p_{i}(0)\}, exact expressions for minimum search time (to determine the one and only one nonzero mean process) are derived. Only one pointimay be observed at a given time, in contrast to the more standard decision theory problem where all n processes are observed simultaneously. The problem is formulated in continuous time, as a limiting case of discrete-time hypothesis tests. The performance of the optimal strategy is shown to be far superior to the performance of some standard strategies.