Disjunctive List-Decoding Codes

A binary code of size $t$ and length $N$ is said to be a disjunctive list-decoding code (LD-code) of strength $s$ with list size $L$, $s+L < t$, if it is an incidence matrix of a family of $t$ subsets of $N$-set where the union of any $s$ sets does not contain the union of any other $L$ sets of this family. The purpose of this work is to develop probabilistic and combinatorial methods for obtaining new lower and upper asymptotic bounds on the maximal size $t(s,L,N)$ of LD-codes and their generalizations called LD-hypercodes. Such codes are considered in the problems of nonadaptive group testing, transmitting messages through a multiple access channel, fingerprinting digital data and some other applications of information theory and coding theory.