In this paper, we introduce the concept of biprojectivity in studying the cryptographically
important almost perfect nonlinear (APN) functions. Although several known families of …

A well-known conjecture due to van Lint and MacWilliams states that if A is a subset of F q 2
such that 0, 1∈ A,| A|= q, and a− b is a square for each a, b∈ A, then A must be the subfield …

Abstract Let GP (q 2, m) be the m-Paley graph defined on the finite field with order q 2. We
study eigenfunctions and maximal cliques in generalised Paley graphs GP (q 2, m), where …

Let $ GP (q, d) $ be the $ d $-Paley graph defined on the finite field $\mathbb {F} _q $. It is
notoriously difficult to improve the trivial upper bound $\sqrt {q} $ on the clique number of …

We describe a new class of maximal cliques, with a vector space structure, of Cayley graphs
defined on the additive group of a field. In particular, we show that in the cubic Paley graph …

We prove that a family of pseudo-Paley graphs of square order obtained from unions of
cyclotomic classes satisfies the Erd\H {o} s-Ko-Rado (EKR) module property, in a sense that …

It is known that Paley graphs of square order have the strict-EKR property, that is, all
maximum cliques are canonical cliques. Peisert-type graphs are natural generalizations of …

The celebrated Erdős–Ko–Rado (EKR) theorem for Paley graphs of square order states that
all maximum cliques are canonical in the sense that each maximum clique arises from the …

We derive an asymptotic formula for the number of solutions in a given subfield to certain
system of equations over finite fields. As an application, we construct new families of …

An important problem on almost perfect nonlinear (APN) functions is the existence of APN
permutations on even-degree extensions of F 2 larger than 6. Browning et al.(2010) gave …