A multiary (polyadic, n-ary) quasigroup is an n-ary operation which is invertible with respect to each of its variables. A biased expansion of a graph is a kind of branched covering graph with additional structure similar to combinatorial homotopy of circles. A biased expansion of a circle with chords encodes a multiary quasigroup, the chords corresponding to factorizations, i.e., associative s...

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...

In this correspondence, we investigate two important structural properties of block 2tary PSK modulation codes, namely: linear structure and phase symmetry. For an AWGN channel, the error performance of a modulation code depends on its squared Euclidean distance distribution. Linear structure of a code makes the error performance analysis much easier. Phase symmetry of a code is important in re...

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 paper presents a new fast k-ary reduction for integer GCD. It enjoys powerful properties and improves on the running time of the quite similar integer GCD algorithm of Kannan et al. Our k-ary reduction also improves on Sorenson's k-ary reductionn14] and thus favorably matches We-ber's algorithmm15]. More generally, the fast k-ary reduction also provides a basic tool for almost all the best ...

7-hydroxy-5,4'-dimethoxy-2-arylbenzofuran (Ary) is purified from Livistona. It has been demonstrated to have anticancer activity to various tumors in including cervical cancer, but its mechanism is still unclear. In the present, we show that Ary induces cervical cancer cells apoptosis through mitochondria degradation and mediates cervical cancer cell arrest. Further, Ary-inducing cell cycle G1/...

In this paper from q-ary perfect codes new completely regular q-ary codes are constructed. In particular, two new ternary completely regular codes are obtained from ternary Golay [11, 6, 5] code. The first [11, 5, 6] code with covering radius ρ = 4 coincides with the dual Golay code and its intersection array is (22, 20, 18, 2, 1; 1, 2, 9, 20, 22) . The second [10, 5, 5] code, with covering rad...

We consider perfect 1-error correcting codes over a finite field with q elements (briefly q-ary 1-perfect codes). In this paper, a generalized concatenation construction for q-ary 1-perfect codes is presented that allows us to construct q-ary 1-perfect codes of length (q − 1)nm + n +m from the given q-ary 1-perfect codes of length n = (q1 − 1)/(q − 1) and m = (q2 − 1)/(q − 1), where s1, s2 are ...

A non-decreasing sequence of positive integer weights P ={p1, p2,..., pn} (n = N*(m-1) + 1, N is number of non-leaves of m-ary tree) is called absolutely ordered if the intermediate sequences of weights produced by m-ary Huffman algorithm for initial sequence P on i-th step satisfy the following conditions 2 , , ) ( 1 ) ( − = < + N 0 i p p i m i m . Let T be an m-ary tree of size n and M=M(T) b...

In this paper we study the expressive power of k-ary exclusion logic, EXC[k], that is obtained by extending first order logic with k-ary exclusion atoms. It is known that without arity bounds exclusion logic is equivalent with dependence logic. From the translations between them we see that the expressive power of EXC[k] lies in between k-ary and (k+1)-ary dependence logics. We will show that, ...