Internal and external partial difference families and cyclotomy
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We introduce the concept of a disjoint partial difference family (DPDF) and an external partial difference family (EPDF), a natural generalization of the much-studied disjoint difference family (DDF), external difference family (EDF) and partial difference set (PDS). We establish properties and indicate connections to other recently-studied combinatorial structures. We show how DPDFs and EPDFs may be formed from PDSs, and present various cyclotomic constructions for DPDFs and EPDFs. As part of this, we develop a unified cyclotomic framework, which yields some known results on PDSs, DDFs and EDFs as special cases.
Huczynska , S & Johnson , L 2023 , ' Internal and external partial difference families and cyclotomy ' , Discrete Mathematics , vol. 346 , no. 3 , 113295 . https://doi.org/10.1016/j.disc.2022.113295
Copyright © 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
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