for a finite group G, we denote by p(G) the minimal degree of faithful permutation representations of G, and denote by c(G), the minimal degree of faithful representation of G by quasi-permutation matrices over the complex field C. In this paper we will assume that, G is a p-group of exponent p and class 2, where p is prime and cd(G) = {1, |G : Z(G)|^1/2}. Then we will s...

We consider rational functions of the form V(x)/U(x), where both V(x) and U(x) are relatively prime polynomials over finite field \(\mathbb {F}_q\). Polynomials that permute elements a field, called permutation (PPs), have been subject research for decades. Let \({\mathcal {P}}^1(\mathbb {F}_q)\) denote {F}_q\cup \{\infty \}\). If function, permutes {F}_q)\), it is function (PRF). \(N_d(q)\) nu...

Permutation polynomials over finite fields play important roles in finite fields theory. They also have wide applications in many areas of science and engineering such as coding theory, cryptography, combinational design, communication theory and so on. Permutation binomials and trinomials attract people’s interest due to their simple algebraic form and additional extraordinary properties. In t...

The Discrete Memory Machine (DMM) is a theoretical parallel computing model that captures the essence of the shared memory access of GPUs. The bank conflicts should be avoided for maximizing the bandwidth of the shared memory access. Offline permutation of an array is a task to copy all elements in array a into array b along a permutation given in advance. The main contribution of this paper is...