Rectangular, range, and restricted AONTs: Three generalizations of all-or-nothing transforms

<p style='text-indent:20px;'>All-or-nothing transforms (AONTs) were originally defined by Rivest [<xref ref-type="bibr" rid="b14">14</xref>] as bijections from <inline-formula><tex-math id="M1">\begin{document}$ s $\end{document}</tex-math></inline-formula> input blocks to <inline-formula><tex-math id="M2">\begin{document}$ s $\end{document}</tex-math></inline-formula> output blocks such that no information can be obtained about any input block in the absence of any output block. Numerous generalizations and extensions of all-or-nothing transforms have been discussed in recent years, many of which are motivated by diverse applications in cryptography, information security, secure distributed storage, etc. In particular, <inline-formula><tex-math id="M3">\begin{document}$ t $\end{document}</tex-math></inline-formula>-AONTs, in which no information can be obtained about any <inline-formula><tex-math id="M4">\begin{document}$ t $\end{document}</tex-math></inline-formula> input blocks in the absence of any <inline-formula><tex-math id="M5">\begin{document}$ t $\end{document}</tex-math></inline-formula> output blocks, have received considerable study.</p><p style='text-indent:20px;'>In this paper, we study three generalizations of AONTs that are motivated by applications due to Pham et al. [<xref ref-type="bibr" rid="b13">13</xref>] and Oliveira et al. [<xref ref-type="bibr" rid="b12">12</xref>]. We term these generalizations rectangular, range, and restricted AONTs. Briefly, in a rectangular AONT, the number of outputs is greater than the number of inputs. A range AONT satisfies the <inline-formula><tex-math id="M6">\begin{document}$ t $\end{document}</tex-math></inline-formula>-AONT property for a range of consecutive values of <inline-formula><tex-math id="M7">\begin{document}$ t $\end{document}</tex-math></inline-formula>. Finally, in a restricted AONT, the unknown outputs are assumed to occur within a specified set of "secure" output blocks. We study existence and non-existence and provide examples and constructions for these generalizations. We also demonstrate interesting connections with combinatorial structures such as orthogonal arrays, split orthogonal arrays, MDS codes and difference matrices.</p>

Bounds for the Minimum Distance and Covering Radius of Orthogonal Arrays via Their Distance Distributions

We propose two methods for obtaining estimations on the minimum distance and covering radius of orthogonal arrays. Both methods are based on knowledge about the (feasible) sets of distance distributions of orthogonal arrays with given length, cardinality, factors and strength. New bounds are presented either in analytic form and as products of an ongoing project for computation and investigation of the possible distance distributions of orthogonal arrays with parameters in doable ranges.

Quantum combinatorial designs and k-uniform states

Goyeneche et al.\ [Phys.\ Rev.\ A \textbf{97}, 062326 (2018)] introduced several classes of quantum combinatorial designs, namely quantum Latin squares, quantum Latin cubes, and the notion of orthogonality on them. They also showed that mutually orthogonal quantum Latin arrangements can be entangled in the same way in which quantum states are entangled. Moreover, they established a relationship between quantum combinatorial designs and a remarkable class of entangled states called $k$-uniform states, i.e., multipartite pure states such that every reduction to $k$ parties is maximally mixed. In this article, we put forward the notions of incomplete quantum Latin squares and orthogonality on them and present construction methods for mutually orthogonal quantum Latin squares and mutually orthogonal quantum Latin cubes. Furthermore, we introduce the notions of generalized mutually orthogonal quantum Latin squares and generalized mutually orthogonal quantum Latin cubes, which are equivalent to quantum orthogonal arrays of size $d^2$ and $d^3$, respectively, and thus naturally provide $2$- and $3$-uniform states.

Transesterification Optimization using Calcium Oxide from Karanja Oil and Results Validation by ANN

Biodiesel is obtained using the transesterification process from renewable oils obtained from vegetable and animal fats. The transesterification process is used to produce biodiesel from Karanja oil with heterogeneous catalyst Calcium Oxide (CaO). In this research work, the Taguchi method has used for the optimization of the transesterification process using five input parameters and five levels for the development of orthogonal arrays. Experiments have conducted as per the L25 orthogonal array developed by Taguchi and yields obtained have been noted. The results obtained by experimentation have been analyzed by Minitab software. The results from Minitab have compared with the results obtained using ANN script analytically as well as graphically. The maximum value of yield has 88% at optimum parametric value namely molar ratio 20% with the addition of 3% Calcium oxide catalyst at process temperature 65ºC for 60 minutes reaction time and agitation speed 600 rpm.

New Waste-Based Composite Material for Construction Applications

The global demand for fiber-based products is continuously increasing. The increased consumption and fast fashion current in the global clothing market generate a significant quantity of pre-and post-production waste that ends up in landfills and incinerators. The present study aims to obtain a new waste-based composite material panel for construction applications with improved mechanical properties that can replace traditional wood-based oriented strand boards (OSB). The new composite material is formed by using textile wastes as a reinforcement structure and a combination of bi-oriented polypropylene films (BOPP) waste, polypropylene non-woven materials (TNT) waste and virgin polypropylene fibers (PP) as a matrix. The mechanical properties of waste-based composite materials are modeled using the Taguchi method based on orthogonal arrays to maximize the composite characteristics’ mechanical properties. Experimental data validated the theoretical results obtained.