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    Existence and non-existence results for Strong External Difference Families

    Paterson, Maura B. and Huczynska, S. (2016) Existence and non-existence results for Strong External Difference Families. Working Paper. Birkbeck, University of London, London, UK.

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    Abstract

    We consider strong external difference families (SEDFs); these are external difference families satisfying additional conditions on the patterns of external differences that occur, and were first defined in the context of classifying optimal strong algebraic manipulation detection codes. We establish new necessary conditions for the existence of (n, m, k, �)-SEDFs; in particular giving a near-complete treatment of the � = 2 case. For the case m = 2, we obtain a structural characterization for partition type SEDFs (of maximum possible k and �), showing that these correspond to Paley partial difference sets. We also prove a version of our main result for generalized SEDFs, establishing non-trivial necessary conditions for their existence.

    Metadata

    Item Type: Monograph (Working Paper)
    Additional Information: Birkbeck Pure Mathematics Preprint Series #27
    School: Birkbeck Schools and Departments > School of Business, Economics & Informatics > Economics, Mathematics and Statistics
    Research Centre: Applied Macroeconomics, Birkbeck Centre for
    Depositing User: Administrator
    Date Deposited: 22 Mar 2019 13:16
    Last Modified: 27 Jul 2019 10:28
    URI: http://eprints.bbk.ac.uk/id/eprint/26753

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