Partial Geometric Difference Families

Ölmez

2015

Des. Codes Cryptogr.

Self Cite

Combinatorial designs have long been used to design efficient statistical experiments. More recently, connections to the theory of cryptographic communications have emerged. Combinatorial designs have provided solutions to problems coming from signal processing, radar, error-correcting codes, optical orthogonal codes, and image processing. Further, the most elegant solutions have come from designs with prescribed automorphisms. In this paper, we focus on partial geometric designs, a generalization of the classical 2-design. These designs have recently been shown to produce two directed strongly regular graphs. We generalize the well-known Kramer-Mesner Theorem for 2-designs to partial geometric designs. We also construct infinite families of partial geometric designs admitting a group of automorphisms which acts regularly on the point set and semi-regularly on the block set. The designs are obtained from new constructions of partial geometric difference families. These families were recently introduced a generalization of both the classical difference family and the partial geometric difference set.

Section: Preliminariesmentioning

confidence: 98%

Section: Partial Geometric Difference Family Constructionsmentioning

confidence: 99%

Section: Definitionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Partial geometric designs with prescribed automorphisms

Ölmez

2015

Des. Codes Cryptogr.

Self Cite

“…The equivalence between partial geometric difference families and partial geometric designs admitting a group of automorphisms which acts regularly on the point set and semi-regularly on the block set was established in [44].…”

Section: Introductionmentioning

confidence: 99%

Partial geometric designs and difference families

Hogben, and Zhijun Wu. I would also like to thank my family for their love and encouragement. It has been a long road but I am finally here. Thank you for always believing in me. I would also like to thank all my friends in the math department. You were my first collaborators and partners on this crazy journey. Finally, I would like to thank Juan Marcos Brandi. You were my family for the last five years, standing beside me through the good times and the bad.

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

J of Combinatorial Designs

Ölmez

Song

2016

Self Cite

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.