A framework for constructing partial geometric difference sets

Davis J. A., Olmez O.

DESIGNS CODES AND CRYPTOGRAPHY, vol.86, no.6, pp.1367-1375, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 86 Issue: 6
  • Publication Date: 2018
  • Doi Number: 10.1007/s10623-017-0400-2
  • Journal Name: DESIGNS CODES AND CRYPTOGRAPHY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1367-1375
  • Keywords: Difference sets, Partial geometric difference sets, Partial geometric designs, Building sets, Extended building sets
  • Ankara University Affiliated: Yes

Abstract

Partial geometric difference sets (PGDSs) were defined in Olmez (J Combin Des 22(6):252-269, 2014). They are used to construct partial geometric designs. We use the framework of extended building sets to find infinite families of PGDSs in abelian groups. Included in our new families of PGDSs are generalizations of the Hadamard, McFarland, Spence, Davis-Jedwab, and Chen difference sets.