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dc.contributor.authorHuczynska, Sophie
dc.contributor.authorPaterson, Maura B.
dc.identifier.citationHuczynska , S & Paterson , M B 2018 , ' Existence and non-existence results for strong external difference families ' , Discrete Mathematics , vol. 341 , no. 1 , pp. 87-95 .
dc.identifier.otherPURE: 251126953
dc.identifier.otherPURE UUID: b6658fa3-203f-4ad3-97b3-3b5504007c79
dc.identifier.otherRIS: urn:CBBC53C677BA522798F5ABB2C4E8F934
dc.identifier.otherScopus: 85029570292
dc.identifier.otherWOS: 000414113100010
dc.identifier.otherORCID: /0000-0002-0626-7932/work/74117793
dc.descriptionThe first author is supported by a Research Incentive Grant from The Carnegie Trust for the Universities of Scotland (Grant No. 70582).en
dc.description.abstractWe 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 , λ) -SEDFs; in particular giving a near-complete treatment of the λ = 2 case. For the case m = 2 , we obtain a structural characterization for partition type SEDFs (of maximum possible k and λ), 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.
dc.relation.ispartofDiscrete Mathematicsen
dc.rights© 2017, Elsevier. 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 may differ slightly from the final published version. The final published version of this work is available at
dc.subjectStrong external difference familyen
dc.subjectAMD codeen
dc.subjectQA Mathematicsen
dc.titleExistence and non-existence results for strong external difference familiesen
dc.typeJournal articleen
dc.contributor.sponsorCarnegie Trusten
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.description.statusPeer revieweden

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