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

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Title: Probabilistic Methods for Deriving New Lower Bounds on the Rates of Locally Thin Families and Weak Superimposed Codes.
Authors: Goshkoder, D. Yu.1 (AUTHOR) daniilgoshkoder@mail.ru
Source: Problems of Information Transmission. Sep2025, Vol. 61 Issue 2, p73-94. 22p.
Subjects: Coding theory, Superimposed coding, Mathematical statistics, Mathematical bounds
Abstract: 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. [ABSTRACT FROM AUTHOR]
Copyright of Problems of Information Transmission is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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PubType: Academic Journal
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  Data: 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. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Problems of Information Transmission is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1134/S0032946025020012
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      – Code: eng
        Text: English
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      – SubjectFull: Superimposed coding
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      – SubjectFull: Mathematical statistics
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