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 language | English |
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Pages (from-to) | 103-127 |
Number of pages | 25 |
Journal | Designs, Codes and Cryptography |
Volume | 78 |
Early online date | 28 Nov 2015 |
DOIs | |
Publication status | Published - Jan 2016 |
Keywords
- Frequency hopping sequences, difference families, m-sequences, finite geometry