New constructions for disjoint partial difference families and external partial difference families
Abstract
Recently, new combinatorial structures called disjoint partial difference families (DPDFs) and external partial difference families (EPDFs) were introduced, which simultaneously generalize partial difference sets, disjoint difference families and external difference families, and have applications in information security. So far, all known construction methods have used cyclotomy in finite fields. We present the first noncyclotomic infinite families of DPDFs which are also EPDFs, in structures other than finite fields (in particular cyclic groups and nonabelian groups). As well as direct constructions, we present an approach to constructing DPDFs/EPDFs using relative difference sets (RDSs); as part of this, we demonstrate how the well-known RDS result of Bose extends to a very natural construction for DPDFs and EPDFs.
Citation
Huczynska , S & Johnson , L 2024 , ' New constructions for disjoint partial difference families and external partial difference families ' , Journal of Combinatorial Designs , vol. 32 , no. 4 , pp. 190-213 . https://doi.org/10.1002/jcd.21930
Publication
Journal of Combinatorial Designs
Status
Peer reviewed
ISSN
1063-8539Type
Journal article
Description
Funding: The research of Sophie Huczynska is supported by EPSRC grant EP/X021157/1.Collections
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