In this paper, we generalize some existing results on Boolean functions to the q-ary functions defined over Zq, where q ≥ 2 is an integer, and obtain some new characterization of q-ary functions based on spectral analysis. We provide a relationship between WalshHadamard spectra of two p-ary functions f and g (for p a prime) and their derivative Df,g. We provide a relationship between the Walsh-...

The paper deals with the perfect 1-error correcting codes over a finite field with q elements (briefly q-ary 1-perfect codes). We show that the orthogonal code to the q-ary non-full-rank 1-perfect code of length n = (q − 1)/(q − 1) is a q-ary constant-weight code with Hamming weight equals to qm−1 where m is any natural number not less than two. We derive necessary and sufficient conditions for...

We present the first algorithm for learning n-ary node selection queries in trees from completely annotated examples by methods of grammatical inference. We propose to represent n-ary queries by deterministic n-ary node selecting tree transducers (n-NSTTs). These are tree automata that capture the class of monadic second-order definable nary queries. We show that n-NSTT defined polynomially bou...

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...