# New results on non-disjoint and classical strong external difference families

## TL;DR

This paper introduces new constructions for combinatorial structures called SEDFs, which are useful in information security and communications.

## Contribution

The paper presents new constructions for classical and non-disjoint SEDFs using a sequence-based framework.

## Key findings

- Constructions encompass all known non-cyclotomic examples of classical and non-disjoint SEDFs.
- New external difference structures are introduced, allowing varying set-sizes and multisets.
- Applications of these structures are demonstrated in communications.

## Abstract

Classical strong external difference families (SEDFs) are much-studied combinatorial structures motivated by information security applications; it is conjectured that only one classical abelian SEDF exists with more than two sets. Recently, non-disjoint SEDFs were introduced; it was shown that families of these exist with arbitrarily many sets. We present constructions for both classical and non-disjoint SEDFs, which encompass all known non-cyclotomic examples for either type (plus many new examples) using a sequence-based framework. Moreover, we introduce a range of new external difference structures (allowing set-sizes to vary, and sets to be replaced by multisets) in both the classical and non-disjoint case, and show how these may be applied to various communications applications.