Strong difference families of special types

TL;DR

This paper introduces strong difference families of special types to generate new combinatorial designs and constructs various applications including group divisible designs, rotational BIBDs, and optical orthogonal codes with specific parameters.

Contribution

It presents a novel class of strong difference families and demonstrates their use in constructing multiple combinatorial and optical design structures.

Findings

Constructed group divisible designs of type 30^u with block size 6.

Derived r-rotational BIBDs with block size 6 for r=6,10.

Obtained several classes of optimal optical orthogonal codes with weights 5 to 8.

Abstract

Strong difference families of special types are introduced to produce new relative difference families from the point of view of both asymptotic existences and concrete examples. As applications, group divisible designs of type $30^u$ with block size $6$ are discussed, $r$-rotational balanced incomplete block designs with block size $6$ are derived for $r\in\{6,10\}$, and several classes of optimal optical orthogonal codes with weight $5$, $6$, $7$, or $8$ are obtained.