A d-hypercube of order n is an n × · · · × nd (d times) array with n elements from a set Q of cardinality n. We recall several connections between d-hypercubes of order n and d-ary operations of order n. We give constructions of orthogonal d-ary operations that generalize a result of Belyavskaya and Mullen. Our main result is a general construction of d-orthogonal d-ary operations from d-ary qu...

This paper concerns a relationship between soft sets and n-ary polygroups. We consider the notion of an n-ary polygroup as a generalization of a polygroup and apply the notion of soft sets to n-ary polygroups. Some related notions are defined and several basic properties are discussed by using the soft set theory. Furthermore, we propose the homomorphism of n-ary polygroups and investigate the ...

In this paper, we define the strongly compatible relation ε on the (m,n)ary hypermodule M, so that the quotient (M/ε∗, h/ε∗) is an (m,n)-ary module over the fundamental (m,n)-ary ring (R/Γ∗, f/Γ∗, g/Γ∗). Also, we determine a family P (M) of subsets of an (m,n)-ary hypermodule M and we give a sufficient condition such that the geometric space (M,P (M)) is strongly transitive. Mathematics Subject...

In this paper, using bent functions defined on the finite field, we generalized the construction method of the family of p-ary bent sequences with balanced and optimal correlation property introduced by Kumar and Moreno for an odd prime p [3], called a generalized p-ary bent sequence. It turns out that the family of balanced p-ary sequences with optimal correlation property introduced by Moriuc...

The h-extra connectivity is an important parameter to measure the reliability and fault tolerance ability of large interconnection networks. The k-ary ncube is an important interconnection network of parallel computing systems. The 1-restricted connectivity of k-ary n-cubes has been obtained by Chen et al. for k ≥ 4 in [6]. Nevertheless, the h-extra connectivity of 3-ary ncubes has not been obt...

This effort focuses on the comparison of On Off Keying (OOK) to incoherent 4-ary Amplitude Shift Keying (ASK). We show that a 0.4 bits/s/Hz improvement in spectral efficiency is obtained by utilising 4-ary ASK. We determined the filter steepness required to achieve this maximum obtainable spectral efficiency. The comparison of OOK and 4-ary ASK in terms of dispersion tolerance for Non-Return-to...

This paper exploits for the first time use of machine learning (ML) based techniques to identify complex structured light patterns under free space optics (FSO) jamming attacks secure FSO-based applications. Five M-ary modulation schemes, construed using Laguerre and Hermite Gaussian (LG HG) mode families, were used in this investigation. These include 8-ary LG, superposition-LG, 16-ary HG, LG ...

The performance analysis of free space optical communication (FSO) systems using relays and spatial diversity at the transmitter end is presented in this paper. The impact of atmospheric turbulence and attenuation caused by different weather conditions and geometric losses has also been taken into account. The effect of turbulence is modeled over a log-normal probability density function. We pr...

In lattice theory, lattice polynomials have been defined as well-formed expressions involving variables linked by the lattice operations ∧ and ∨ in an arbitrary combination of parentheses. In turn, such expressions naturally define lattice polynomial functions. For instance, p(x1, x2, x3) = (x1 ∧ x2) ∨ x3 is a 3-ary lattice polynomial function. The concept of lattice polynomial function can be ...

From a generic set of uncertain pieces of information about the normal course of things and a temporal sequence of reported facts, an intelligent artifact should be able to identify causally related events and distinguish between factors that facilitate or justify the occurrence of events from other facts. In this paper, we propose a model for causality and facilitation ascriptions when the bac...