Ken W. Smith

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5 papers · 1 filter

math.CO2023

Nonabelian partial difference sets constructed using abelian techniques

James Davis, John Polhill, Ken Smith +1

A $(v, k, λ, μ)$ -partial difference set (PDS) is a subset $D$ of a group $G$ such that $∣ G ∣ = v$ , $∣ D ∣ = k$ , and every nonidentity element $x$ of $G$ can be written in either $λ$ or…

math.CO2023

Genuinely nonabelian partial difference sets

John Polhill, James Davis, Ken Smith +1

Strongly regular graphs (SRGs) provide a fertile area of exploration in algebraic combinatorics, integrating techniques in graph theory, linear algebra, group theory, finite fields…

math.CO2022

Sets of mutually orthogoval projective and affine planes

Charles J. Colbourn, Colin Ingalls, Jonathan Jedwab +3

A pair of planes, both projective or both affine, of the same order and on the same pointset are orthogoval if each line of one plane intersects each line of the other plane in at…

math.CO2018

Partial Difference Sets in $C_{2^{n}} \times C_{2^{n}}$

Martin E. Malandro, Ken W. Smith

We give an algorithm for enumerating the regular nontrivial partial difference sets (PDS) in the group $G_{n} = C_{2^{n}} \times C_{2^{n}}$ . We use our algorithm to obtain all of these PD…

math.CO2018

All $(96, 20, 4)$ difference sets and related structures

Omar A. AbuGhneim, Dylan Peifer, Ken W. Smith

In 1978, Robert Kibler at the National Security Agency in Fort Meade, Maryland published a description of all noncyclic difference sets with $k < 20$ . Kibler's decision to stop his…

Nonabelian partial difference sets constructed using abelian techniques

Genuinely nonabelian partial difference sets

Sets of mutually orthogoval projective and affine planes

Partial Difference Sets in C2n​×C2n​

All (96,20,4) difference sets and related structures

Partial Difference Sets in $C_{2^{n}} \times C_{2^{n}}$

All $(96, 20, 4)$ difference sets and related structures