Internal and external partial difference families and cyclotomy
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Abstract
We introduce the concept of a disjoint partial difference family (DPDF) and an external partial difference family (EPDF), a natural generalisation of the much-studied structures of disjoint difference family (DDF), external difference family (EDF) and partial difference set (PDS). We establish properties and constructions, and indicate connections to other recently-studied combinatorial structures. We show how DPDFs and EPDFs may be formed from collections of PDSs, and also present cyclotomic methods yielding DPDFs and EPDFs whose component sets are not in general PDSs. As part of this, we develop a unified framework encompassing various known constructions for cyclotomic difference structures, which also yields new results on DDFs and EDFs.Keywords
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This publication has 23 references indexed in Scilit:
- Construction and nonexistence of strong external difference familiesJournal of Algebraic Combinatorics, 2018
- Cyclotomic construction of strong external difference families in finite fieldsDesigns, Codes and Cryptography, 2017
- Near-complete external difference familiesDesigns, Codes and Cryptography, 2016
- External Difference Families from Finite FieldsJournal of Combinatorial Designs, 2016
- Disjoint difference families and their applicationsDesigns, Codes and Cryptography, 2015
- Cyclotomic constructions of external difference families and disjoint difference familiesJournal of Combinatorial Designs, 2009
- Constructions of External Difference Families and Disjoint Difference FamiliesDesigns, Codes and Cryptography, 2006
- Some Notes on the Linear Complexity of Sidel’nikov-Lempel-Cohn-Eastman SequencesDesigns, Codes and Cryptography, 2006
- On simple radical difference familiesJournal of Combinatorial Designs, 1995
- A survey of partial difference setsDesigns, Codes and Cryptography, 1994