A character theoretic approach to planar functions

DOI10.1007/s12095-011-0044-4zbMath1282.12004OpenAlexW2061710385MaRDI QIDQ662195

Alexander Pott, Yue Zhou

Publication date: 21 February 2012

Published in: Cryptography and Communications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12095-011-0044-4

zbMATH Keywords

planar functionrelative difference setsemifield

Mathematics Subject Classification ID

Polynomials over finite fields (11T06) Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.) (05B10) Semifields (12K10) Finite geometry and special incidence structures (51E99)

Related Items (6)

Investigating rational perfect nonlinear functions ⋮ Almost perfect and planar functions ⋮ Finite semifields and nonsingular tensors ⋮ More constructions of APN and differentially 4-uniform functions by concatenation ⋮ On homogeneous planar functions ⋮ Another class of perfect nonlinear polynomial functions

Cites Work

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• Planar functions and planes of Lenz-Barlotti class II
• A family of skew Hadamard difference sets
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• Ovoids of parabolic spaces
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• A new family of semifields with 2 parameters
• New semifields, PN and APN functions
• Relating three nonlinearity parameters of vectorial functions and building APN functions from bent functions
• Commutative presemifields and semifields
• Proof of the prime power conjecture for projective planes of order 𝑛 with abelian collineation groups of order 𝑛²
• The weights of the orthogonals of the extended quadratic binary Goppa codes
• A new APN function which is not equivalent to a power mapping
• New Perfect Nonlinear Multinomials over F $_{p^{2k}}$ for Any Odd Prime p
• Two Classes of Quadratic APN Binomials Inequivalent to Power Functions
• On the Dual of Monomial Quadratic p-ary Bent Functions
• On Nonassociative Division Algebras

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