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    Weighted external difference families and R-optimal AMD codes

    Huczynska, S. and Paterson, Maura B. (2018) Weighted external difference families and R-optimal AMD codes. Technical Report. Birkbeck, University of London, London, UK.

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    Abstract

    In this paper, we provide a mathematical framework for characterizing AMD codes that are R-optimal. We introduce a new combinatorial object, the reciprocally-weighted external difference family (RWEDF), which corresponds precisely to an R-optimal weak AMD code. This definition subsumes known examples of existing optimal codes, and also encompasses combinatorial objects not covered by previous definitions in the literature. By developing structural group-theoretic characterizations, we exhibit infinite families of new RWEDFs, and new construction methods for known objects such as near-complete EDFs. Examples of RWEDFs in non-abelian groups are also discussed.

    Metadata

    Item Type: Monograph (Technical Report)
    Additional Information: Birkbeck Pure Mathematics Preprint Series #40
    School: School of Business, Economics & Informatics > Economics, Mathematics and Statistics
    Depositing User: Administrator
    Date Deposited: 22 Mar 2019 09:58
    Last Modified: 17 Jun 2021 10:37
    URI: https://eprints.bbk.ac.uk/id/eprint/26787

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