Internal and external partial difference families and cyclotomy

DOI10.1016/j.disc.2022.113295zbMath1506.05035arXiv2201.07553OpenAlexW4313443339MaRDI QIDQ2111939

Laura M. Johnson, Sophie Huczynska

Publication date: 17 January 2023

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2201.07553

zbMATH Keywords

partial difference setcyclotomydisjoint difference familydisjoint partial difference familyexternal difference familyexternal partial difference family

Mathematics Subject Classification ID

Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.) (05B10)

Uses Software

• GAP

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On disjoint \((v,k,k-1)\) difference families
• Combinatorial characterizations of algebraic manipulation detection codes involving generalized difference families
• Partial difference sets
• Constructions of external difference families and disjoint difference families
• Disjoint difference families and their applications
• Difference systems of sets and cyclotomy
• Constructions of almost difference families
• Uniform cyclotomy
• A survey of partial difference sets
• Partitions and other coverings of finite groups.
• New combinatorial designs and their applications to authentication codes and secret sharing schemes.
• Weighted external difference families and R-optimal AMD codes
• Cyclotomic construction of strong external difference families in finite fields
• New existence and nonexistence results for strong external difference families
• Novák's conjecture on cyclic Steiner triple systems and its generalization
• A note on difference families from cyclotomy
• Near-complete external difference families
• Some notes on the linear complexity of Sidel'nikov-Lempel-Cohn-Eastman sequences
• On supplementary difference sets
• Cyclotomy and difference families in elementary Abelian groups
• Construction and nonexistence of strong external difference families
• On the number of solutions of \(u^k+D\equiv w^2 \pmod p\)
• Cyclotomic constructions of external difference families and disjoint difference families
• The Geometry of Two-Weight Codes
• Resolution of the sign ambiguity in the determination of the cyclotomic numbers of order 4 and the corresponding Jacobsthal sum.
• On simple radical difference families
• Cyclotomic difference sets in finite fields
• Cyclotomy, Higher Congruences, and Waring's Problem
• Packings of partial difference sets
• External Difference Families from Finite Fields

This page was built for publication: Internal and external partial difference families and cyclotomy