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<p>We study combinatorial structures known in coding theory: locally thin families of sets and weak superimposed codes. Using expurgated random coding methods, we obtain new lower bounds on the rates of the considered constructions, which generalize and improve previously known results. Furthermore, we consider traceability multimedia fingerprinting codes resistant to averaging attack and adversarial noise. We demonstrate new lower bounds on their rates, which follow from the obtained rate estimates for weak superimposed codes.</p>

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Probabilistic Methods for Deriving New Lower Bounds on the Rates of Locally Thin Families and Weak Superimposed Codes

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • D. Yu. Goshkoder

摘要

We study combinatorial structures known in coding theory: locally thin families of sets and weak superimposed codes. Using expurgated random coding methods, we obtain new lower bounds on the rates of the considered constructions, which generalize and improve previously known results. Furthermore, we consider traceability multimedia fingerprinting codes resistant to averaging attack and adversarial noise. We demonstrate new lower bounds on their rates, which follow from the obtained rate estimates for weak superimposed codes.