A new family of semifields with 2 parameters

Abstract

A new family of commutative semifields with two parameters is presented. Its left and middle nucleus are both determined. Furthermore, we prove that for any different pairs of parameters, these semifields are not isotopic. It is also shown that, for some special parameters, one semifield in this family can lead to two inequivalent planar functions. Finally, using similar construction, new APN functions are given.

References in corpus (4)

• Construction of Additive Reed-Muller Codes
• An extension of the order bound for AG codes
• Explicit Evaluation of Certain Exponential Sums of Quadratic Functions over ${\mathbb{F}}_{p^n}$, $p$ Odd
• A Note on the Isotopism of Commutative Semifields

Cited by in corpus (9)

• On kernels and nuclei of rank metric codes
• New Semifields and new MRD Codes from Skew Polynomial Rings
• Linearly Self-Equivalent APN Permutations in Small Dimension
• Symplectic spreads, planar functions and mutually unbiased bases
• Semifields, relative difference sets, and bent functions
• A lower bound on the number of inequivalent APN functions
• The number of almost perfect nonlinear functions grows exponentially
• Two new infinite classes of APN functions
• New Perfect Nonlinear Functions and Their Semifields