UR Scholarship Repository

Title

New Constructions of Divisible Designs

Authors

James A. Davis, University of RichmondFollow

DOI

10.1016/0012-365X(93)90586-I

Abstract

A construction is given for a (p^2a(p+1),p²,p^2a+1(p+1),p^2a+1,p^2a(p+1)) (p a prime) divisible difference set in the group H×Z²_pa+1 where H is any abelian group of order p+1. This can be used to generate a symmetric semi-regular divisible design; this is a new set of parameters for λ₁≠0, and those are fairly rare. We also give a construction for a (p^a−1+p^a−2+…+p+2,p^a+2, p^a(p^a+p^a−1+…+p+1), p^a(p^a−1+…+p+1), p^a−1(p^a+…+p²+2)) divisible difference set in the group H×Z_p2×Z^a_p. This is another new set of parameters, and it corresponds to a symmetric regular divisible design. For p=2, these parameters have λ₁=λ₂, and this corresponds to the parameters for the ordinary Menon difference sets.

Document Type

Article

Publication Date

9-12-1993

Publisher Statement

Copyright © 1993, Elsevier. This article first appeared in Discrete Mathematics: 120:1-3 (1993), 261-268.

Please note that downloads of the article are for private/personal use only.

Recommended Citation

Davis, James A. "New Constructions of Divisible Designs." Discrete Mathematics 120, no. 1-3 (September 12, 1993): 261-68. doi: 10.1016/0012-365X(93)90586-I.