Construction of cyclic codes over \mathbb F _2+u\mathbb F _2 for DNA computing

We construct codes over the ring $\mathbb F _2+u\mathbb F _2$ with $u^2=0$ for use in DNA computing applications. The codes obtained satisfy the reverse complement constraint, the $GC$ content constraint, and avoid the secondary structure. They are derived from cyclic reverse-complement codes over the ring $\mathbb F _2+u\mathbb F _2$ . We also construct an infinite family of BCH DNA codes.     

One weight $$\mathbb {Z}_2\mathbb {Z}_4$$ additive codes

We study one weight \(\mathbb {Z}_2\mathbb {Z}_4\) additive codes. It is shown that the image of an equidistant \(\mathbb {Z}_2\mathbb {Z}_4\) code is a binary equidistant code and that the image of a one weight \(\mathbb {Z}_2\mathbb {Z}_4\) additive code, with nontrivial binary part, is a linear binary one weight code. The structure and possible weights for all one weight \(\mathbb {Z}_2\mathbb {Z}_4\) additive codes are described. Additionally, a lower bound for the minimum distance of dual codes of one weight additive codes is obtained.     

Cyclic codes over $${\mathbb {F}}_{2^m}[u]/\langle u^k\rangle $$ of oddly even length

Let \({\mathbb {F}}_{2^m}\) be a finite field of characteristic 2 and \(R={\mathbb {F}}_{2^m}[u]/\langle u^k\rangle ={\mathbb {F}}_{2^m} +u{\mathbb {F}}_{2^m}+\ldots +u^{k-1}{\mathbb {F}}_{2^m}\) (\(u^k=0\)) where \(k\in {\mathbb {Z}}^{+}\) satisfies \(k\ge 2\). For any odd positive integer n, it is known that cyclic codes over R of length 2n are identified with ideals of the ring \(R[x]/\langle x^{2n}-1\rangle \). In this paper, an explicit representation for each cyclic code over R of length 2n is provided and a formula to count the number of codewords in each code is given. Then a formula to calculate the number of cyclic codes over R of length 2n is obtained. Moreover, the dual code of each cyclic code and self-dual cyclic codes over R of length 2n are investigated.     

Cryptanalysis of a key exchange protocol based on the endomorphisms ring End{(\mathbb{Z}_{p} \times \mathbb{Z}_{p^2})}

Climent et?al. (Appl Algebra Eng Commun Comput 22:91?C108, 2011) identified the elements of the endomorphisms ring End ${(\mathbb{Z}_p \times \mathbb{Z}_{p^2})}$ with elements in a set, E _p , of matrices of size 2?× 2, whose elements in the first row belong to ${\mathbb{Z}_{p}}$ and the elements in the second row belong to ${\mathbb{Z}_{p^2}}$ . By taking advantage of matrix arithmetic, they proposed a key exchange protocol using polynomial functions over E _p defined by polynomials in ${\mathbb{Z}[X]}$ . In this note, we show that this protocol is insecure; it can be broken by solving a set of 10 consistent homogeneous linear equations in 8 unknowns over ${\mathbb{Z}_{p^2}}$ .     

On quasi-cyclic codes over {\mathbb{Z}_q}

Quasi-cyclic (QC) codes are a remarkable generalization of cyclic codes. Many QC codes have been shown to be best for their parameters. In this paper, some structural properties of QC codes over the prime power integer residue ring ${\mathbb{Z}_q}$ are considered. An l-QC code of length lm over ${\mathbb{Z}_q}$ is viewed both as in the conventional row circulant form and also as a ${\frac{\mathbb{Z}_q[x]}{\langle x^m-1 \rangle}}$ -submodule of ${\frac{GR(q,l)[x]}{\langle x^m-1 \rangle}}$ , where GR(q, l) is the Galois extension ring of degree l over ${\mathbb{Z}_q}$ . A necessary and sufficient condition for cyclic codes over Galois rings to be free is obtained and a BCH type bound for them is also given. A sufficient condition for 1-generator QC codes to be ${\mathbb{Z}_q}$ -free is given and a formula to evaluate their ranks is derived. Some distance bounds for 1-generator QC codes are also discussed. The duals of QC codes over ${\mathbb{Z}_q}$ are also briefly discussed.     

Two new permutation polynomials with the form {\left(x^{2^k}+x+\delta\right)^{s}+x} over {\mathbb{F}_{2^n}}

This note presents two new permutation polynomials with the form ${p(x)=\left(x^{2^k}+x+\delta\right)^{s}+x}$ over the finite field ${\mathbb{F}_{2^n}}$ as a supplement of the recent work of Yuan, Ding, Wang and Pieprzyk.     

New constructions of APN polynomial functions in odd characteristic

A general construction of APN polynomial functions of the form \(c_{30}x^3+c_{03}x^{3q}+\sum \nolimits _{i=0}^2\sum \nolimits _{j=0}^2c_{ij}x^{i+qj}\) over a finite field \(\mathbb {F}_{q^2}\) of odd characteristic is proposed, and some variants of this construction are also presented. As a consequence, new APN polynomial functions such as ones over \(\mathbb {F}_{3^{2m}}\) and \(\mathbb {F}_{11^2}\) which are CCZ-inequivalent to known APN functions are obtained.     

An extension of the (strong) primitive normal basis theorem

An extension of the primitive normal basis theorem and its strong version is proved. Namely, we show that for nearly all \(A = {\small \left( \begin{array}{cc} a&{}b \\ c&{}d \end{array} \right) } \in \mathrm{GL}_2(\mathbb {F}_{q})\) , there exists some \(x\in \mathbb {F}_{q^m}\) such that both \(x\) and \((-dx+b)/(cx-a)\) are simultaneously primitive elements of \(\mathbb {F}_{q^m}\) and produce a normal basis of \(\mathbb {F}_{q^m}\) over \(\mathbb {F}_q\) , granted that \(q\) and \(m\) are large enough.     

Further crosscorrelation properties of sequences with the decimation factor {d=\frac{p^n+1}{p+1}-\frac{p^n-1}{2}}

For an odd integer n ≥ 3, an odd prime p ≡ 3(mod4) and ${d=\frac{p^n+1}{p+1}-\frac{p^n-1}{2}}$ , the value distribution of the exponential sum ${\sum\limits_{x\in \mathbb{F}_{p^n}^{\,*}}\omega^{Tr^n_1(x-\gamma x^{d})}\,(\gamma\in \mathbb{F}_{p^n}^{*})}$ is completely determined in this paper, where ω is a primitive complex p-th root of unity. This improves the results of Müller (1999) and Hu et al. (2001) about the crosscorrelation of sequences with the decimation factor d.     

Application of Non-Isothermal Thermogravimetric Method to Interpret the Decomposition Kinetics of \hbox {NaNO}_{3}, \hbox {KNO}_{3}, and \hbox {KClO}_{4}

The non-isothermal thermogravimetric method was used to study the thermal decomposition of \(\hbox {KClO}_{4}, \hbox {KNO}_{3}\) , and \(\hbox {NaNO}_{3}\) at heating rates of (5, 10, 15, and 20)  \(\hbox {K}\cdot \hbox {min}^{-1}\) . The activation energy of thermal decomposition reactions was computed by isoconversional methods of Ozawa–Flynn–Wall, Kissinger–Akahiro–Sunose, and Friedman equations. Also, the kinetic triplet of the thermal decomposition of salts was determined by the model-fitting method of the modified Coats–Redfern equation. The activation energies of \(\hbox {KClO}_{4}, \hbox {KNO}_{3}\) , and \(\hbox {NaNO}_{3}\) of (293 to 307, 160 to 209, and 192 to 245)  \(\hbox {kJ}\cdot \hbox {mol}^{-1}\) , respectively, are obtained by non–isothermal isoconversional methods. The modified Coats and Redfern method showed that the most probable mechanism functions \(g(\alpha )\) of \([-\hbox {ln}(1 - \alpha )]^{1/3}\) (model A3: Arami–Erofeev equation) and \((1 - \alpha )^{-1}- 1\) (model F2: second order) can be used to predict the decomposition mechanisms of \(\hbox {KClO}_{4}\) , \(\hbox {KNO}_{3}\) , and \(\hbox {NaNO}_{3}\) , respectively.     

Impact of Associated Gases on Equilibrium and Transport Properties of a \mathrm{CO}_{2} Stream: Molecular Simulation and Experimental Studies

During the various carbon dioxide capture and storage (CCS) stages, an accurate knowledge of thermodynamic properties of \(\mathrm{CO}_{2}\) streams is required for the correct sizing of plant units. The injected \(\mathrm{CO}_{2}\) streams are not pure and often contain small amounts of associated gaseous components such as \(\mathrm{O}_{2}, \mathrm{N}_{2}\) , \(\mathrm{SO}_{x}, \mathrm{NO}_{x}\) , noble gases, etc. In this work, the thermodynamic behavior and transport properties of some \(\mathrm{CO}_{2}\) -rich mixtures have been investigated using both experimental approaches and molecular simulation techniques such as Monte Carlo and molecular dynamics simulations. Using force fields available in the literature, we have validated the capability of molecular simulation techniques in predicting properties for pure compounds, binary mixtures, as well as multicomponent mixtures. These validations were performed on the basis of experimental data taken from the literature and the acquisition of new experimental data. As experimental data and simulation results were in good agreement, we proposed the use of simulation techniques to generate new pseudo-experimental data and to study the impact of associated gases on the properties of \(\mathrm{CO}_{2}\) streams. For instance, for a mixture containing 92.0 mol% of \(\mathrm{CO}_{2}\) , 4.0 mol% of \(\mathrm{O}_{2}\) , 3.7 mol% of Ar, and 0.3 mol% of \(\mathrm{N}_{2}\) , we have shown that the presence of associated gases leads to a decrease of 14 % and 21 % of the dense phase density and viscosity, respectively, as compared to pure \(\mathrm{CO}_{2}\) properties.     

1-generator quasi-cyclic codes over finite chain rings

Let R be an arbitrary commutative finite chain ring with $1\ne 0$ . 1-generator quasi-cyclic (QC) codes over R are considered in this paper. Let $\gamma $ be a fixed generator of the maximal ideal of R, $F=R/\langle \gamma \rangle $ and $|F|=q$ . For any positive integers m, n satisfying $\mathrm{gcd}(q,n)=1$ , let $\mathcal{R}_n=R[x]/\langle x^n-1\rangle $ . Then 1-generator QC codes over R of length mn and index m can be regarded as 1-generator $\mathcal{R}_n$ -submodules of the module $\mathcal{R}_n^m$ . First, we consider the parity check polynomial of a 1-generator QC code and the properties of the code determined by the parity check polynomial. Then we give the enumeration of 1-generator QC codes with a fixed parity check polynomial in standard form over R. Finally, under the condition that $\mathrm{gcd}(|q|_n,m)=1$ , where $|q|_n$ denotes the order of q modulo n, we describe an algorithm to list all distinct 1-generator quasi-cyclic codes with a fixed parity check polynomial in standard form over R of length mn and index m.     

Primitive elements with prescribed trace

Let \(q\) be a power of a prime number \(p\) . Let \(n\) be a positive integer. Let \(\mathbb {F}_{q^n}\) denote a finite field with \(q^n\) elements. In this paper, we consider the existence of the some specific elements in the finite field \(\mathbb {F}_{q^n}\) . We get that when \(n\ge 29\) , there are elements \(\xi \in \mathbb {F}_{q^n}\) such that \(\xi +\xi ^{-1}\) is a primitive element of \(\mathbb {F}_{q^n}\) , and \(\mathrm{Tr}(\xi ) = a, \mathrm{Tr}(\xi ^{-1}) = b\) for any pair of prescribed \(a, b \in \mathbb {F}_q^*\) .     

Elastic Properties of Monoclinic \hbox {ZrO}_{2} at Finite Temperatures Via First Principles

The structural and elastic properties of orthorhombic $\hbox {ZrO}_{2}\,(m\hbox {-ZrO}_{2})$ as a function of temperature are investigated by the generalized gradient approximation (GGA) correction scheme in the framework of density functional theory (DFT) and the quasi-harmonic Debye model. The thirteen independent elastic constants of $m\hbox {-ZrO}_{2}$ at temperatures to 3200 K are theoretically investigated for the first time. It is found that with increasing temperature, all elastic constants change, especially $C_{35}\hbox { and }C_{25}$ change rapidly in the temperature range of 1400 K to 1600 K and 2200 K to 2600 K, respectively. We also obtain the bulk modulus $B$ , shear modulus $G$ , Young’s moduli $E$ , as well as Poisson’s ratio $\sigma $ of $m\hbox {-ZrO}_{2}$ at high temperatures. Our work suggests that it is very important to predict the melting properties of materials via the elastic constants at temperatures.     

Molecular beam epitaxy of semipolar AlN(11\bar{2}2) and GaN(11\bar{2}2) on m-sapphire

We report on the plasma-assisted molecular-beam epitaxy of semipolar $\hbox{AlN}(11\bar{2}2)$ and GaN( $11\bar{2}2$ ) films on $(1\bar{1}00)$ m-plane sapphire. AlN deposited on m-sapphire settles into two main crystalline orientation domains, $\hbox{AlN}(11\bar{2}2)$ and $\hbox{AlN}(10\bar{1}0),$ whose ratio depends on the III/V ratio. Growth under moderate nitrogen-rich conditions enables to isolate the $(11\bar{2}2)$ orientation. The in-plane epitaxial relationships of $\hbox{AlN}(11\bar{2}2)$ on m-plane sapphire are $[11\bar{2}\bar{3}]_{\rm AlN} \vert \vert [0001]_{\rm sapphire}$ and $[1\bar{1}00]_{\rm AlN} \vert \vert [11\bar{2}0]_{\rm sapphire}.$ GaN deposited directly on m-sapphire results in ( $11\bar{2}2$ )-oriented layers with ( $10\bar{1}\bar{3}$ )-oriented inclusions. A ～100 nm-thick AlN( $11\bar{2}2$ ) buffer imposes the ( $11\bar{2}2$ )-orientation for the GaN layer grown on top. By studying the Ga-desorption on GaN( $11\bar{2}2$ ), we conclude that these optimal growth conditions corresponds to a Ga excess of one monolayer on the GaN( $11\bar{2}2$ ) surface.     

\text{ CO}_{2} Laser-Based Pulsed Photoacoustic Ammonia Detection

Detecting ammonia traces is relevant in health, manufacturing, and security areas, among others. As ammonia presents a strong absorption band (the $\nu _{2}$ mode) around 10  $\upmu $ m, some of the physical properties which may influence its detection by means of pulsed photoacoustic (PA) spectroscopy with a TEA $\text{ CO}_{2}$ laser have been studied. The characteristics of the ammonia molecule and the laser intensity may result in a nonlinear dependence of the PA signal amplitude on the laser fluence. Ammonia absorption can be described as a simple two-level system with power broadening. As $\text{ NH}_{3}$ is a polar molecule, it strongly undergoes adsorption phenomena in contact with different surfaces. Therefore, physical adsorption–desorption at the cell’s wall is studied. A theoretical model, based on Langmuir’s assumptions, fits well to the experimental results with stainless steel. Related to these studies, measurements led to the conclusion that, at the used fluenced values, dissociation by multiphotonic absorption at the 10P(32) laser line may be discarded. A calibration of the system was performed, and a detection limit around 190 ppb (at 224 $\text{ mJ}\cdot \text{ cm}^{-2}$ ) was achieved.     

Study of Structural Modification and Fluctuation Induced Electrical Conductivity in \text {YBa}_{2}\text {Cu}_{3}\text {O}_{7-y}+x \text {BaSnO}_{3} Superconductor Composite

A series of \((1-x) \text {YBa}_{2}\text {Cu}_{3}\text {O}_{7-y} + x \text {BaSnO}_{3 }(x = 0.0, 0.1, 0.3, 0.5, 1.0, 2.5, 5.0\,\text {wt}{\%})\) samples were prepared using the solid-state reaction method. XRD graphs confirm the orthorhombic structure in pristine as well as in composite samples. Raman spectra show the presence of all the vibration modes in pure as well as in the composite samples. In addition, some defect-induced modes have also appeared in the higher weight % BSO-added sample, and no loss of apical oxygen O(4) at 500 cm \(^{-1}\) occurs due to BaSnO \(_{3}\) (BSO) addition. Microstructural analysis reveals the unchanged grain size with the incorporation of dielectric BSO particles in the YBCO matrix. Superconducting transition temperature determined from standard four-probe method decreases with the increase of BSO wt%. Excess conductivity fluctuation analysis using Aslamazov–Larkin model fitting reveals transition of two dominant regions (2D and 3D) above \(T_\mathrm{c}\) . 2D to 3D crossover temperature i.e. Lawrence–Doniach temperature that demarcates dimensional nature of fluctuation inside the grains is influenced by BSO incorporation in YBCO matrix.     

Effect of Previous Milling of Precursors on Magnetoelectric Effect in Multiferroic {\mathrm{Bi}_{5}\mathrm{Ti}_{3}\mathrm{FeO}_{15}} Ceramic

$\mathrm{Bi}_{5}\mathrm{Ti}_{3}\mathrm{FeO}_{15}$ Bi 5 Ti 3 FeO 15 magnetoelectric (ME) ceramics have been synthesized and investigated. The ME effect can be described as an induced electric polarization under an external magnetic field or an induced magnetization under an external electric field. The materials in the ME effect are called ME materials, and they are considered to be a kind of new promising materials for sensors, processors, actuators, and memory systems. Multiferroics, the materials in which both ferromagnetism and ferroelectricity can coexist, are the prospective candidates which can potentially host the gigantic ME effect. $\mathrm{Bi}_{5}\mathrm{Ti}_{3}\mathrm{FeO}_{15}$ Bi 5 Ti 3 FeO 15 , an Aurivillius compound, was synthesized by sintering a mixture of $\mathrm{Bi}_{2}\mathrm{O}_{3}, \mathrm{Fe}_{2}\mathrm{O}_{3}$ Bi 2 O 3 , Fe 2 O 3 , and $\mathrm{TiO}_{2}$ TiO 2 oxides. The precursor materials were prepared in a high-energy attritorial mill for (1, 5, and 10) h. The orthorhombic $\mathrm{Bi}_{5}\mathrm{Ti}_{3}\mathrm{FeO}_{15}$ Bi 5 Ti 3 FeO 15 ceramics were obtained by a solid-state reaction process at 1313 K. The ME voltage coefficient ( $\alpha _\mathrm{ME}$ α ME ) was measured using the dynamic lock-in method. The highest ME voltage coefficient ( $\alpha _\mathrm{ME} = 8.28\,\text{ mV }{\cdot }\text{ cm }^{-1}{\cdot }\text{ Oe }^{-1})$ α ME = 8.28 mV · cm ? 1 · Oe ? 1 ) is obtained for the sample milled for 1 h at $H_\mathrm{DC }= 4$ H DC = 4  Oe (1 Oe = 79.58  $\text{ A }{\cdot }\text{ m }^{-1})$ A · m ? 1 ) .     

High-pressure studies of superconductivity in $$\hbox {BiO}_{0.75}\hbox {F}_{0.25}\hbox {BiS}_{2}$$

\(\hbox {BiO}_{0.75}\hbox {F}_{0.25}\hbox {BiS}_{2}\) crystallizes in tetragonal CeOBiS\(_{2}\) structure (S. G. P4/nmm). We have investigated the effect of pressure on magnetization measurements. Our studies suggest improved superconducting properties in polycrystalline samples of \(\hbox {BiO}_{0.75}\hbox {F}_{0.25}\hbox {BiS}_{2}\). The \(T_{\mathrm{c}}\) in our sample is 5.3 K, at ambient pressure, which is marginal but definite enhancement over \(T_{\mathrm{c}}\) reported earlier (= 5.1 K). The upper critical field \(H_{\mathrm{c}2}\)(0) is greater than 3 T, which is higher than earlier report on this material. As determined from the M–H curve, both \(H_{\mathrm{c}2}\) and \(H_{\mathrm{c}1}\) decrease under external pressure P (0 \(\le P \le \) 1 GPa). We observe a decrease in critical current density and transition temperature on applying pressure in \(\hbox {BiO}_{0.75}\hbox {F}_{0.25}\hbox {BiS}_{2}\).