•  
  •  
 

Turkish Journal of Mathematics

DOI

10.3906/mat-2104-5

Abstract

Plateaued (vectorial) functions over finite fields have diverse applications in symmetric cryptography, coding theory, and sequence theory. Constructing these functions is an attractive research topic in the literature. We can distinguish two kinds of constructions of plateaued functions: secondary constructions and primary constructions. The first method uses already known functions to obtain new functions while the latter do not need to use previously constructed functions to obtain new functions. In this work, the first secondary constructions of (non)weakly regular plateaued (vectorial) functions are presented over the finite fields of odd characteristics. We also introduce some recursive constructions of (non)weakly regular plateaued $p$-ary functions by using already known such functions. We obtain nontrivial plateaued functions from the previously known trivial plateaued (partially bent) functions in the proposed construction methods.

Keywords

$p$-ary functions, plateaued functions, (non)weakly regular plateaued functions, secondary construction

First Page

2295

Last Page

2306

Download

Included in

Mathematics Commons

Share

COinS