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    Characterising bimodal collections of sets in finite groups

    Huczynska, Sophie and Paterson, Maura (2019) Characterising bimodal collections of sets in finite groups. Technical Report. Birkbeck, University of London, London, UK.

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    Abstract

    A collection of disjoint subsets A = {A 1 ,A 2 ,...,A m } of a finite abelian group is said to have the bimodal property if, for any non-zero group element δ, either δ never occurs as a difference between an element of A i and an element of some other set A j , or else for every element a i in A i there is an element a j ∈ A j for some j 6= i such that a i − a j = δ. This property arises in various familiar situations, such as the cosets of a fixed subgroup or in a group partition, and has applications to the construction of optimal algebraic manipulation detection (AMD) codes. In this paper, we obtain a structural characterisation for bimodal collections of sets.

    Metadata

    Item Type: Monograph (Technical Report)
    Additional Information: Birkbeck Pure Mathematics Preprint Series #49
    School: School of Business, Economics & Informatics > Economics, Mathematics and Statistics
    Depositing User: Maura Paterson
    Date Deposited: 15 Jun 2020 10:46
    Last Modified: 14 Feb 2021 23:06
    URI: https://eprints.bbk.ac.uk/id/eprint/32250

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