It is impossible to introduce combinatorial designs and linear codes without basic tools in
certain mathematical areas. In this chapter, we give a brief introduction to cyclotomy, finite …

Permutation polynomials over finite fields — A survey of recent advances - ScienceDirect Skip
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This is the first monograph on codebooks and linear codes from difference sets and almost
difference sets. It aims at providing a survey of constructions of difference sets and almost …

Two-to-one (2-to-1) mappings over finite fields play an important role in symmetric
cryptography. In particular they allow to design APN functions, bent functions and semi-bent …

Strongly regular graphs from unions of cyclotomic classes Page 1 Journal of Combinatorial
Theory, Series B 102 (2012) 982–995 Contents lists available at SciVerse ScienceDirect …

We revisit the old idea of constructing difference sets from cyclotomic classes. Two
constructions of skew Hadamard difference sets are given in the additive groups of finite …

A packing of partial difference sets is a collection of disjoint partial difference sets in a finite
group $ G $. This configuration has received considerable attention in design theory, finite …

In this paper, two-to-one mappings and involutions without any fixed point on finite fields of
even characteristic are investigated. First, we characterize a closed relationship between …

For each odd prime power q, we present two rational functions f ( X ) ∈ F q ( X ) \documentclass[12pt]{minimal}
\usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} …

Permutation polynomials have been extensively studied for their applications in
cryptography, coding theory, combinatorial design, etc. An important subfamily of …