Let Ω = {1, 2, . . . , n} where n 2. The shape of an ordered set partition P = (P1, . . . , Pk) of Ω is the integer partition λ = (λ1, . . . , λk) defined by λi = |Pi|. Let G be a group of permutations acting on Ω. For a fixed partition λ of n, we say that G is λ-transitive if G has only one orbit when acting on partitions P of shape λ. A corresponding definition can also be given when G is jus...

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...

We are concern about a conjecture proposed in the middle of the seventies by Hellesseth in the framework of maximal sequences and theirs crosscorrelations. The conjecture claims the existence of a zero outphase Fourier coefficient. We give some divisibility properties in this direction. 1. Two conjectures of Helleseth Let L be a finite field of order q > 2 and characteristic p. Let μ be the can...

Questions about order versus disorder in systems and models have been fascinating scientists over the years. In Computer Science, order is intimately related to sorting, commonly meant as the task of arranging keys in increasing or decreasing order with respect to an underlying total order relation. The sorted organization is amenable for searching a set of n keys, since each search requires Θ(...

In this article we construct an irreducible simple subgroup G = 〈q, y, t, w〉 of GL8671(13) from an irreducible subgroup T of GL11(2) isomorphic to Mathieu’s simple group M24 by means of Algorithm 2.5 of [13]. We also use the first author’s similar construction of Fischer’s sporadic simple group G1 = Fi23 described in [11]. He starts from an irreducible subgroup T1 of GL11(2) contained in T whic...

Blind source separation presents an interest for several applications fields. In this study, focus is on the blind separation of biomechanical signals namely ground reaction force signals. We showed recently in [1, 2], that ground reaction force signals are cyclostationary. Thus, the idea of this paper is to make use of the cyclostationary character of ground reaction force signals to separate ...

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...