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

Sophie Huczynska; Sophie Hume

doi:10.1007/s10623-025-01566-3

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

Sophie Huczynska^*, Sophie Hume

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	1985-2012
Number of pages	28
Journal	Designs, Codes and Cryptography
Volume	93
Issue number	6
Early online date	5 Feb 2025
DOIs	https://doi.org/10.1007/s10623-025-01566-3
Publication status	Published - Jun 2025

Keywords

Strong external difference family
Non-disjoint strong external difference family
Binary sequences
Optical orthogonal codes
AMD codes

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Final published version, 560 KBLicence: CC BY

New Directions in AMD Codes over Galois: New directions in AMD codes over Galois fields and related structures
Huczynska, S. (PI)
EPSRC
1/01/23 → 31/12/23
Project: Standard

Cite this

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title = "New results on non-disjoint and classical strong external difference families",

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.",

keywords = "Strong external difference family, Non-disjoint strong external difference family, Binary sequences, Optical orthogonal codes, AMD codes",

author = "Sophie Huczynska and Sophie Hume",

note = "Funding: The first author was funded by EPSRC Grant EP/X021157/1. The second author was funded by the London Mathematical Society Grant URB-2023-75.",

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doi = "10.1007/s10623-025-01566-3",

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AB - 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.

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KW - Non-disjoint strong external difference family

KW - Binary sequences

KW - Optical orthogonal codes

KW - AMD codes

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DO - 10.1007/s10623-025-01566-3

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JO - Designs, Codes and Cryptography

JF - Designs, Codes and Cryptography

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ER -

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

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Keywords

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New Directions in AMD Codes over Galois: New directions in AMD codes over Galois fields and related structures

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