Near-complete external difference families

James A. Davis*, Sophie Huczynska, Gary L. Mullen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)
2 Downloads (Pure)

Abstract

We introduce and explore near-complete external difference families, a partitioning of the nonidentity elements of a group so that each nonidentity element is expressible as a difference of elements from distinct subsets a fixed number of times. We show that the existence of such an object implies the existence of a near-resolvable design. We provide examples and general constructions of these objects, some of which lead to new parameter families of near-resolvable designs on a non-prime-power number of points. Our constructions employ cyclotomy, partial difference sets, and Galois rings.

Original languageEnglish
Pages (from-to)415-424
Number of pages10
JournalDesigns, Codes and Cryptography
Volume84
Issue number3
Early online date30 Aug 2016
DOIs
Publication statusPublished - Sept 2017

Keywords

  • Difference family
  • Galois rings
  • Partial difference sets

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