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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. Technical Report. Birkbeck, University of London, London, UK.

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    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.


    Item Type: Monograph (Technical Report)
    Additional Information: Birkbeck Pure Mathematics Preprint Series #27
    School: Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences
    Depositing User: Administrator
    Date Deposited: 22 Mar 2019 13:16
    Last Modified: 09 Aug 2023 12:46


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