Non-disjoint strong external difference families can have any number of sets

Sophie Huczynska; Siaw-Lynn Ng

doi:10.1007/s00013-024-01982-2

Non-disjoint strong external difference families can have any number of sets

Sophie Huczynska^*, Siaw-Lynn Ng

^*Corresponding author for this work

Pure Mathematics

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

Abstract

Strong external difference families (SEDFs) are much-studied combinatorial objects motivated by an information security application. A well-known conjecture states that only one abelian SEDF with more than 2 sets exists. We show that if the disjointness condition is replaced by non-disjointness, then abelian SEDFs can be constructed with more than 2 sets (indeed any number of sets). We demonstrate that the non-disjoint analogue has striking differences to, and connections with, the classical SEDF and arises naturally via another coding application.

Original language	English
Number of pages	11
Journal	Archiv der Mathematik
Early online date	30 Apr 2024
DOIs	https://doi.org/10.1007/s00013-024-01982-2
Publication status	E-pub ahead of print - 30 Apr 2024

Keywords

Strong external difference families
External difference families
Binary sequences
Optical orthogonal codes

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Huczynska_2024_ArchMath_Non-disjoint-strong-external_CC
Copyright © 2024 The Author(s). Open Access: This article is licensed under a Creative Commons Attribution 4.0 International License (https://creativecommons. org/licenses/by/4.0/.), which permits use, sharing, adaptation, distribution and re- production in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regu- lation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
Final published version, 328 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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abstract = "Strong external difference families (SEDFs) are much-studied combinatorial objects motivated by an information security application. A well-known conjecture states that only one abelian SEDF with more than 2 sets exists. We show that if the disjointness condition is replaced by non-disjointness, then abelian SEDFs can be constructed with more than 2 sets (indeed any number of sets). We demonstrate that the non-disjoint analogue has striking differences to, and connections with, the classical SEDF and arises naturally via another coding application.",

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author = "Sophie Huczynska and Siaw-Lynn Ng",

note = "Funding: Engineering and Physical Sciences Research Council (Grant number EP/X021157/1).",

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N2 - Strong external difference families (SEDFs) are much-studied combinatorial objects motivated by an information security application. A well-known conjecture states that only one abelian SEDF with more than 2 sets exists. We show that if the disjointness condition is replaced by non-disjointness, then abelian SEDFs can be constructed with more than 2 sets (indeed any number of sets). We demonstrate that the non-disjoint analogue has striking differences to, and connections with, the classical SEDF and arises naturally via another coding application.

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KW - External difference families

KW - Binary sequences

KW - Optical orthogonal codes

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Non-disjoint strong external difference families can have any number of sets

Abstract

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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