A lower bound for generalized superimposed codes with application to group testing with inhibitors

Abstract

It has been introduced a new generalization of superimposed codes that finds application to the design of efficient algorithms for a variant of group testing known as group testing with inhibitors (GTI). Families associated to these codes have the property that for every q + Sigma_i=1 ^s p_i pairwise different members F₁ ¹,hellip,F_p1 ¹,hellip, F₁ ^s,hellip,F_ps ^s,G₁, hellip,G_q of the family it holds cap_i=1 ^s cup_j=1 ^pi F_j ⁱ nsube cup_i=1 ^q G_j. In this paper we present a lower bound on the minimum length of the generalized superimposed codes of A. De Bonis.