A family of Alltop Functions that are EA-Inequivalent to the Cubic Function

Abstract

Let F be a field. A transformation f of F is called planar if f(a+x) - f(x) is a permutation of F for every nonzero a.

The transformation f is called an Alltop function (or a planar difference function) if f(a+x) -f(x) is planar for every nonzero a.The paper describes a new family of Alltop functions on fields of order that is a (2r)th power of a prime p, p at least 5,where 3 does not divide q+1, where q is the rth power of p.

Keywords

• family
• Alltop
• Functions
• that
• are
• EA-Inequivalent
• Cubic
• Function