Disjoint difference families and their applications

Siaw-Lynn Ng, Maura Beth Paterson

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Abstract

Difference sets and their generalisations to difference families arise from the study of designs and many other applications. Here we give a brief survey of some of these applications, noting in particular the diverse definitions of difference families and the variations in priorities in constructions. We propose a definition of disjoint difference families that encompasses these variations and allows a comparison of the similarities and disparities. We then focus on two constructions of disjoint difference families arising from frequency hopping sequences and show that they are in fact the same. We conclude with a discussion of the notion of equivalence for frequency hopping sequences and for disjoint difference families.
Original languageEnglish
Pages (from-to)103-127
Number of pages25
JournalDesigns, Codes and Cryptography
Volume78
Early online date28 Nov 2015
DOIs
Publication statusPublished - Jan 2016

Keywords

  • Frequency hopping sequences, difference families, m-sequences, finite geometry

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