Abstract:
Locally thin families of sets and weak disjunctive codes are studied. The main result is obtaining new lower bounds on the rates of the studied constructions using probabilistic methods. Additionally, new lower bounds on the rates of multimedia codes that determine the coalition under averaging and noise attacks are presented, which follow from the obtained estimates for the rates of weak disjunctive codes.
Keywords:locally thin families, weak disjunctive codes, binary ensemble with expurgation, $q$-ary ensemble with expurgation.
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