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    Existence and non-existence results for strong external difference families

    Huczynska, S. and Paterson, Maura B. (2017) Existence and non-existence results for strong external difference families. Discrete Mathematics 341 (1), pp. 87-95. ISSN 0012-365X.

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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; lambda)-SEDFs; in particular giving a near-complete treatment of the lambda = 2 case. For the case m = 2, we obtain a structural characterization for partition type SEDFs (of maximum possible k and lambda), 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: Article
    School: Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences
    Depositing User: Maura Paterson
    Date Deposited: 04 Aug 2017 13:38
    Last Modified: 09 Aug 2023 12:42


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