Bent and vectorial bent functions, partial difference sets, and strongly regular graphs

DOI10.3934/amc.2018041zbMath1417.94129OpenAlexW2892868783MaRDI QIDQ1620969

Wilfried Meidl, Ayça Çeşmelioǧlu

Publication date: 15 November 2018

Published in: Advances in Mathematics of Communications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/amc.2018041

zbMATH Keywords

strongly regular graphWalsh transformbent functionpartial difference setvectorial Boolean functiondual bent function

Mathematics Subject Classification ID

Polynomials over finite fields (11T06) Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.) (05B10) Boolean functions (94D10)

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Packings of partial difference sets ⋮ A survey on \(p\)-ary and generalized bent functions ⋮ Constructions of linear codes with two or three weights from vectorial dual-bent functions ⋮ New results on vectorial dual-bent functions and partial difference sets ⋮ Vectorial bent functions and partial difference sets

Cites Work

• On the dual of (non)-weakly regular bent functions and self-dual bent functions
• Strongly regular graphs constructed from \(p\)-ary bent functions
• Some implications on amorphic association schemes
• Strongly regular graphs associated with ternary bent functions
• Generalized bent functions and their properties
• Construction of strongly regular graphs, two-weight codes and partial geometries by finite fields
• A survey of partial difference sets
• Vectorial bent functions and their duals
• A construction of bent functions from plateaued functions
• Association schemes arising from bent functions
• There Are Infinitely Many Bent Functions for Which the Dual Is Not Bent
• Monomial and quadratic bent functions over the finite fields of odd characteristic
• Perfect nonlinear S-boxes
• A characterization of bent functions in terms of strongly regular graphs
• Spectral analysis of Boolean functions as a graph eigenvalue problem
• Bent Functions
• Partial difference sets from quadratic forms and $p$-ary weakly regular bent functions