A Family of Partial Geometric Designs from Three-Class Association Schemes

Nowak K., Olmez O., Song S. Y.

JOURNAL OF COMBINATORIAL DESIGNS, vol.24, no.12, pp.533-552, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 24 Issue: 12
  • Publication Date: 2016
  • Doi Number: 10.1002/jcd.21518
  • Journal Name: JOURNAL OF COMBINATORIAL DESIGNS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.533-552
  • Keywords: association scheme, orthogonal array, 11/2-design, STRONGLY REGULAR GRAPHS, COMBINATORIAL DESIGNS, PROJECTIVE PLANE, ALGEBRAS
  • Ankara University Affiliated: Yes

Abstract

In this paper, we show that partial geometric designs can be constructed from certain three-class association schemes and ternary linear codes with dual distance three. In particular, we obtain a family of partial geometric designs from the three-class association schemes introduced by Kageyama, Saha, and Das in their article ["Reduction of the number of associate classes of hypercubic association schemes," Ann Inst Statist Math 30 (1978)]. We also give a list of directed strongly regular graphs arising from the partial geometric designs obtained in this paper. (C) 2016 Wiley Periodicals, Inc.