Characterising bimodal collections of sets in finite groups
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Date
09/07/2019Metadata
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Abstract
A collection of disjoint subsets A = {A1, A2, ..., Am} of a finite abelian group has the bimodal property if each non-zero group element δ either never occurs as a difference between an element of Ai and an element of Aj with j ≠ i, or else for every element ai in Ai there is an element aj ∈ Aj for some j ≠ i with ai - aj = δ. This property arises in familiar situations, such as cosets of a fixed subgroup or in a group partition, and has applications to the construction of optimal algebraic manipulation detection codes. In this paper, we obtain a structural characterisation for bimodal collections of sets.
Citation
Huczynska , S & Paterson , M 2019 , ' Characterising bimodal collections of sets in finite groups ' , Archiv der Mathematik , vol. First Online . https://doi.org/10.1007/s00013-019-01361-2
Publication
Archiv der Mathematik
Status
Peer reviewed
ISSN
0003-889XType
Journal article
Rights
© 2019, Springer Nature International AG. This work has been made available online in accordance with the publisher's policies. This is the author created accepted version manuscript following peer review and as such may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1007/s00013-019-01361-2
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