Further results on planar DO functions and commutative semifields

DOI10.1007/s10623-011-9564-3zbMath1272.12021OpenAlexW2017453435MaRDI QIDQ411491

Guobiao Weng, Xiangyong Zeng

Publication date: 4 April 2012

Published in: Designs, Codes and Cryptography (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10623-011-9564-3

zbMATH Keywords

semifieldsdifference setsplanar functionsplanar Dembowski-Ostrom polynomial

Mathematics Subject Classification ID

Polynomials over finite fields (11T06) Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.) (05B10) Semifields (12K10)

Related Items (20)

Quasi-perfect linear codes from planar and APN functions ⋮ Unitals in shift planes of odd order ⋮ Two constructions of approximately symmetric informationally complete positive operator-valued measures ⋮ On the 2-ranks of a class of unitals ⋮ The \textit{crooked} property ⋮ A survey on \(p\)-ary and generalized bent functions ⋮ Finite flag-transitive affine planes with a solvable automorphism group ⋮ Investigating rational perfect nonlinear functions ⋮ A new family of semifields with 2 parameters ⋮ Image sets of perfectly nonlinear maps ⋮ Intersection distribution, non-hitting index and Kakeya sets in affine planes ⋮ Almost perfect and planar functions ⋮ Permutation polynomials with low differential uniformity over finite fields of odd characteristic ⋮ On homogeneous planar functions ⋮ Two-to-one mappings and involutions without fixed points over \(\mathbb{F}_{2^n}\) ⋮ CONSTRUCTING NEW APN FUNCTIONS FROM KNOWN PN FUNCTIONS ⋮ Dembowski-Ostrom polynomials and reversed Dickson polynomials ⋮ On derivatives of planar mappings and their connections to complete mappings ⋮ Symplectic spreads, planar functions, and mutually unbiased bases ⋮ Several classes of polynomials with low differential uniformity over finite fields of odd characteristic

Cites Work

• Planar functions and planes of Lenz-Barlotti class II
• Dembowski-Ostrom polynomials from Dickson polynomials
• A family of skew Hadamard difference sets
• Some results on skew Hadamard difference sets
• A survey of partial difference sets
• Antisymmetric difference sets
• Pseudo-Paley graphs and skew Hadamard difference sets from presemifields
• Commutative presemifields and semifields
• Skew-Hadamard Abelian group difference sets
• Partial Difference Sets
• Some Theorems on Planar Mappings
• On Nonassociative Division Algebras
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