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The determinants of { ± 1 } -matrices are calculated via the oriented hypergraphic Laplacian and summing over incidence generalizations of vertex cycle-covers. These cycle-covers are signed and partitioned into families based on their hyperedge containment. Every non-edge-monic family is shown to contribute a net value of 0 to the Laplacian, while each edge-monic family is shown to sum to the absolute value of the determinant of the original incidence matrix. Simple symmetries are identified as well as their relationship to Hadamard's maximum determinant problem. Finally, the entries of the incidence matrix are reclaimed using only the signs of an adjacency-minimal set of cycle-covers from an edge-monic family. [ABSTRACT FROM AUTHOR]

We define quantum automorphisms and isomorphisms of Hadamard matrices. We show that every Hadamard matrix of size N\ge 4 has quantum symmetries and that all Hadamard matrices of a fixed size are mutually quantum isomorphic. These results pass also to the corresponding Hadamard graphs. We also define quantum Hadamard matrices acting on quantum spaces and bring an example thereof over matrix algebras. [ABSTRACT FROM AUTHOR]

Maximin distance designs and orthogonal designs are two attractive classes of space-filling designs for computer experiments, but their theoretical constructions are challenging, especially the construction of optimal designs in terms of both the maximin distance and orthogonality criteria. This paper presents a systematic method for constructing orthogonal maximin distance designs with flexible numbers of runs and factors. The method is carried out by rotating the subarrays of a saturated two-level regular design in Yates order or its circular shifting version. The principal objective is to construct high-level designs from two-level designs, and the method is effective because the performance of high-level designs is determined by that of two-level designs under both the maximin distance and orthogonality criteria. The proposed method is also generalized by rotating the subarrays of a saturated two-level nonregular design such that the resulting designs have flexible run sizes. Comparison results reveal that the resulting orthogonal designs are well worthy of recommendation under the maximin distance criterion. An illustrative example is provided to show that the proposed designs have a good two-dimensional stratification property. An application is given to present the effectiveness of the proposed designs in building statistical surrogate models. [ABSTRACT FROM AUTHOR]

AbstractScreening experiments often require both continuous and categorical factors. In this article we develop a new class of saturated designs containing m three-level continuous factors and m–1 two-level categorical or continuous factors in n=2m runs, where m≥4 . A key advantage is that these designs are available for any even n≥8 . With effect sparsity or by not making use of all of the two-level columns of the design, we demonstrate via simulation that it is possible to identify up to three active quadratic effects. When n is a multiple of 8, the designs are orthogonal. When n is a multiple of four and not a multiple of 8, the three-level factors are orthogonal to each other and to the two-level factors, and the two-level factors are nearly orthogonal to each other. Finally, when n is a multiple of two, and not a multiple of four or 8, the three-level and two-level factors are nearly orthogonal within those groupings, and orthogonal to each other. We show that even in this latter case, the designs typically have power near one for identifying up to m active main effects when the signal-to-noise ratio is greater than 1.5. [ABSTRACT FROM AUTHOR]

In communication technologies such as digital watermarking, wireless sensor networks (WSNs), and visual light communication (VLC), error-correcting codes are crucial. The Enhanced Hadamard Error-Correcting Code (EHC), which is based on 2D Hadamard Basis Images, is a novel error correction technique that is presented in this study. This technique is used to evaluate the effectiveness of the video watermarking scheme. Even with highly sophisticated embedding techniques, watermarks usually fail to resist such comprehensive attacks because of the extraordinarily high compression rate of approximately 1:200 that is frequently employed in video dissemination. It can only be used in conjunction with a sufficient error-correcting coding method. This study compares the efficacy of the well-known Reed–Solomon Code with this novel technique, the Enhanced Hadamard Error-Correcting Code (EHC), in maintaining watermarks in embedded videos. The main idea behind this newly created multidimensional Enhanced Hadamard Error-Correcting Code is to use a 1D Hadamard decoding approach on the 2D base pictures after they have been transformed into a collection of one-dimensional rows. Following that, the image is rebuilt, allowing for a more effective 2D decoding procedure. Using this technique, it is possible to exceed the theoretical error-correcting capacity threshold of ⌊ d m i n − 1 2 ⌋ bits, where d m i n is the Hamming distance. It may be possible to achieve better results by converting the 2D EHC into a 3D format. The new Enhanced Hadamard Code is used in a video watermarking coding scheme to show its viability and efficacy. The original video is broken down using a multi-level interframe wavelet transform during the video watermarking embedding process. Low-pass filtering is applied to the video stream in order to extract a certain frequency range. The watermark is subsequently incorporated using this filtered section. Either the Reed–Solomon Correcting Code or the Enhanced Hadamard Code is used to protect the watermarks. The experimental results show that EHC far outperforms the RS Code and is very resilient against severe MPEG compression. [ABSTRACT FROM AUTHOR]

In this paper, we give constructions of self-orthogonal codes from orbit matrices of Deza graphs, normally regular digraphs and Deza digraphs in terms of a definition given by Wang and Feng. These constructions can also be applied to adjacency matrices of the mentioned graphs. Since a lot of constructions of Deza graphs, normally regular digraphs and Deza digraphs in the sense of Wang and Feng have been known, the methods presented in this paper give us a rich source of matrices that span self-orthogonal codes. [ABSTRACT FROM AUTHOR]

The theory of uniform design has received increasing interest because of its wide application in the field of computer experiments. The generalized discrete discrepancy is proposed to evaluate the uniformity of the mixed-level factorial design. In this paper, the authors give a lower bound of the generalized discrete discrepancy and provide some construction methods of optimal mixed-level uniform designs which can achieve this lower bound. These methods are all deterministic construction methods which can avoid the complexity of stochastic algorithms. Both saturated mixed-level uniform designs and supersaturated mixed-level uniform designs can be obtained with these methods. Moreover, the resulting designs are also Χ2-optimal and minimum moment aberration designs. [ABSTRACT FROM AUTHOR]

In this paper, a novel signal processing method combining mathematical morphology (MM) and Walsh theory is proposed, which uses Walsh functions to control the structuring element (SE) and MM operators. Based on the Walsh-MM method, a scheme for power quality disturbances detection and classification is developed, which involves three steps: denoising, feature extraction and morphological clustering. First, various evolution rules of Walsh function are used to generate groups of SEs for the multiscale Walsh-ordered morphological operation, so the original signal can be denoised. Next, the fundamental wave of the denoised signal is suppressed by Hadamard matrix; thus, disturbances can be extracted. Finally, the Walsh power spectrum of the waveform extracted in the previous step is calculated, and the parameters of which are taken by morphological clustering to classify the disturbances. Simulation results reveal the proposed scheme can effectively detect and classify disturbances, and the Walsh-MM method is less affected by noise and only involves simple calculation, which has a potential to be implemented in hardware and more suitable for real-time application.

We experimentally demonstrate the use of a multi-plane light converter (MPLC) as a non-mode selective (de)multiplexer for converting Hermite-Gaussian (HG) modes into a Hadamard matrix of fundamental Gaussian spots and vice versa. We interferometrically measure and characterize the complex output of the device and successfully demonstrate the conversion between HG modes and Hadamard matrices of Gaussian spots. The MPLC non-mode selective (de)multiplexers can be useful for versatile control of spatial properties of light beams with potential applications in beam shaping, coherent beam combining, and wavefront synthesis.

In this paper, we give a method for the constructions of Hadamard matrices of composite orders by using suitable T-matrices and known Hadamard matrices. We establish a formula for Tmatrices and Hadamard matrices and discuss under what condition we can get T-matrices from the known Hadamard matrices. [ABSTRACT FROM AUTHOR]

The present work describes the optimization of the composition of liquid culture medium in sub-merged fermentation in batch system by varying 7 factors, according to a Hadamard matrix. The work aimed to determine the optimal values of the varied factors (sugar content, yeast extract, KCl, medium volume (Vw/Vt), inoculation ratio, MgSO4 × 7H2O, vitamins) that conducted to a maximum value of the system response, namely the yeast biomass cell weight, (6.61 g) a parameter relevant from technical and economic point of view. The temperature, stirring rate and air flow rate for the Hadamard matrix were maintained constant for each process variant. Applying the process, an active yeast biomass with a protein content of 36.45 g% was obtained. The active yeast biomass of S. cerevisiae PFE-II-3 was used in a further study to obtain wines at the Pietroasa Viticulture and Winemaking Research and Development Station. [ABSTRACT FROM AUTHOR]

By assuming a type of balance for length ℓ=87\ell =87 and nontrivial subgroups of multiplier groups of Legendre pairs (LPs) for length ℓ=85\ell =85, we find LPs of these lengths. We then study the power spectral density (PSD) values of mm compressions of LPs of length 5m5m. We also formulate a conjecture for LPs of lengths ℓ≡0\ell \equiv 0 (mod 5) and demonstrate how it can be used to decrease the search space and storage requirements for finding such LPs. The newly found LPs decrease the number of integers in the range ≤200\le 200 for which the existence question of LPs remains unsolved from 12 to 10.

Let be the unit cube in and let be the space of continuous functions with the norm By denote the set of polynomials of degree , i. e., the set of linear functions on . The interpolation projector with the nodes is defined by the equalities , . Let be the norm of as an operator from to . If is an Hadamard number, then there exists a nondegenerate regular simplex having the vertices at vertices of . We discuss some approaches to get inequalities of the form for the norm of the corresponding projector . [ABSTRACT FROM AUTHOR]

There is limited literature on screening when some factors are at three levels and others are at two levels. This topic has seen renewed interest of late following the introduction of the definitive screening design structure by Jones and Nachtsheim 2011 and Xiao et al. 2012. Two well-known examples are Taguchi's L18 and L36 designs. However, these designs are limited in two ways. First, they only allow for either 18 or 36 runs, which is restrictive. Second, they provide no protection against bias of the main effects due to active two-factor interactions. In this article, we introduce a family of orthogonal, mixed-level screening designs in multiples of eight runs. Our 16-run design can accommodate up to four continuous three-level factors and up to eight two-level factors. The three-level factors must be continuous, whereas the two-level factors can be either continuous or categorical. All of our designs supply substantial bias protection of the main effects estimates due to active two-factor interactions. [ABSTRACT FROM AUTHOR]

Applying the maximum separable distance (MDS) matrices is one of the most common approaches to meet diffusion layer in modern block ciphers. Using Cauchy and extensions of Cauchy matrices are classical methods to generate MDS matrices. In this paper, using generalized Cauchy matrices, an approach to construct MDS matrices is proposed so that if A is an MDS matrix constructed with the proposed approach and B is a 3 × 3 sub-matrix of A , then interesting connections between the entries of B are introduced. More precisely, every element of the matrix B can be uniquely determined by eight other entries of B . Moreover, using generalized Cauchy matrices and also applying the proposed approach, some common forms of MDS matrices such as Hadamard, circulant and MDS matrices with maximum entries equal to the unit element, have been investigated. [ABSTRACT FROM AUTHOR]

In communication technologies such as digital watermarking, wireless sensor networks (WSNs), and visual light communication (VLC), error-correcting codes are crucial. The Enhanced Hadamard Error-Correcting Code (EHC), which is based on 2D Hadamard Basis Images, is a novel error correction technique that is presented in this study. This technique is used to evaluate the effectiveness of the video watermarking scheme. Even with highly sophisticated embedding techniques, watermarks usually fail to resist such comprehensive attacks because of the extraordinarily high compression rate of approximately 1:200 that is frequently employed in video dissemination. It can only be used in conjunction with a sufficient error-correcting coding method. This study compares the efficacy of the well-known Reed–Solomon Code with this novel technique, the Enhanced Hadamard Error-Correcting Code (EHC), in maintaining watermarks in embedded videos. The main idea behind this newly created multidimensional Enhanced Hadamard Error-Correcting Code is to use a 1D Hadamard decoding approach on the 2D base pictures after they have been transformed into a collection of one-dimensional rows. Following that, the image is rebuilt, allowing for a more effective 2D decoding procedure. Using this technique, it is possible to exceed the theoretical error-correcting capacity threshold of ⌊dmin−12⌋ bits, where dmin is the Hamming distance. It may be possible to achieve better results by converting the 2D EHC into a 3D format. The new Enhanced Hadamard Code is used in a video watermarking coding scheme to show its viability and efficacy. The original video is broken down using a multi-level interframe wavelet transform during the video watermarking embedding process. Low-pass filtering is applied to the video stream in order to extract a certain frequency range. The watermark is subsequently incorporated using this filtered section. Either the Reed–Solomon Correcting Code or the Enhanced Hadamard Code is used to protect the watermarks. The experimental results show that EHC far outperforms the RS Code and is very resilient against severe MPEG compression.

We classify all linear completely regular codes which have covering radius and whose dual are antipodal. For this, we firstly show several properties of such dual codes, which are two-weight codes with weights and . [ABSTRACT FROM AUTHOR]

The q k (full) factorial design with replication λ is the multi-set consisting of λ occurrences of each element of each q -ary vector of length k ; we denote this by λ × [ q ] k. An m × n row-column factorial design q k of strength t is an arrangement of the elements of λ × [ q ] k into an m × n array (which we say is of type I k (m , n , q , t)) such that for each row (column), the set of vectors therein are the rows of an orthogonal array of degree k , size n (respectively, m), q levels and strength t. Such arrays are used in experimental design. In this context, for a row-column factorial design of strength t , all subsets of interactions of size at most t can be estimated without confounding by the row and column blocking factors. In this manuscript we study row-column factorial designs with strength t ≥ 2. Our results for strength t = 2 are as follows. For any prime power q and assuming 2 ≤ M ≤ N , we show that there exists an array of type I k (q M , q N , q , 2) if and only if k ≤ M + N , k ≤ (q M − 1) / (q − 1) and (k , M , q) ≠ (3 , 2 , 2). We find necessary and sufficient conditions for the existence of I k (4 m , n , 2 , 2) for small parameters. We also show that I k + α (2 α b , 2 k , 2 , 2) exists whenever α ≥ 2 and 2 α + α + 1 ≤ k < 2 α b − α , assuming there exists a Hadamard matrix of order 4 b. For t = 3 we focus on the binary case. Assuming M ≤ N , there exists an array of type I k (2 M , 2 N , 2 , 3) if and only if M ≥ 5 , k ≤ M + N and k ≤ 2 M − 1. Most of our constructions use linear algebra, often in application to existing orthogonal arrays and Hadamard matrices. [ABSTRACT FROM AUTHOR]

This paper considers coherent states for the representation of Weyl commutation relations over a field of p-adic numbers. A geometric object, a lattice in vector space over a field of p-adic numbers, corresponds to the family of coherent states. It is proven that the bases of coherent states corresponding to different lattices are mutually unbiased, and that the operators defining the quantization of symplectic dynamics are Hadamard operators. [ABSTRACT FROM AUTHOR]

A new meaningful image encryption algorithm based on compressive sensing (CS) and integer wavelet transformation (IWT) is proposed in this study. First of all, the initial values of chaotic system are encrypted by RSA algorithm, and then they are open as public keys. To make the chaotic sequence more random, a mathematical model is constructed to improve the random performance. Then, the plain image is compressed and encrypted to obtain the secret image. Secondly, the secret image is inserted with numbers zero to extend its size same to the plain image. After applying IWT to the carrier image and discrete wavelet transformation (DWT) to the inserted image, the secret image is embedded into the carrier image. Finally, a meaningful carrier image embedded with secret plain image can be obtained by inverse IWT. Here, the measurement matrix is built by both chaotic system and Hadamard matrix, which not only retains the characteristics of Hadamard matrix, but also has the property of control and synchronization of chaotic system. Especially, information entropy of the plain image is employed to produce the initial conditions of chaotic system. As a result, the proposed algorithm can resist known-plaintext attack (KPA) and chosen-plaintext attack (CPA). By the help of asymmetric cipher algorithm RSA, no extra transmission is needed in the communication. Experimental simulations show that the normalized correlation (NC) values between the host image and the cipher image are high. That is to say, the proposed encryption algorithm is imperceptible and has good hiding effect. [ABSTRACT FROM AUTHOR]

In this note, we report the classification of all symmetric 2-(36, 15, 6) designs that admit an automorphism of order 2 and their incidence matrices generate an extremal ternary self-dual code. It is shown that up to isomorphism, there exists only one such design, having a full automorphism group of order 24, and the ternary code spanned by its incidence matrix is equivalent to the Pless symmetry code. [ABSTRACT FROM AUTHOR]

This paper considers the orthogonal observation matrix design of deterministic compressive sampling (CS). An observation matrix called the weighted truncated Hadamard-modulated wideband converter (WITH-MWC) is deterministically designed based on the truncated Hadamard matrix. This matrix can meet the restricted isometry property (RIP) condition with overwhelming probability by randomly or strategically extracting from a standard Hadamard matrix. Most compressed sampling systems are highly sensitive to noise. To reduce the adverse effects of noise interference, partial specific matrix elements are weighted according to the sparse characteristics of multiband signals, and the recovery probability is provably better than that of the original system and other deterministic observation matrices, especially in the low signal-to-noise ratio scenario. Compared to the random Gaussian and random Bernoulli matrices, WITH-MWC is much easier to implement in hardware. The simulations verify the above analysis. [ABSTRACT FROM AUTHOR]

In 2013, Nebe and Villar gave a series of ternary self-dual codes of length 2 (p + 1) for a prime p congruent to 5 modulo 8. As a consequence, the third ternary extremal self-dual code of length 60 was found. We show that these ternary self-dual codes contain codewords which form a Hadamard matrix of order 2 (p + 1) when p is congruent to 5 modulo 24. In addition, we show that the ternary self-dual codes found by Nebe and Villar are generated by the rows of the Hadamard matrices. We also demonstrate that the third ternary extremal self-dual code of length 60 contains at least two inequivalent Hadamard matrices. [ABSTRACT FROM AUTHOR]

Single-pixel cameras offer improved performance in non-visible imaging compared with modern digital cameras which capture images with an array of detector pixels. However, the quality of the images reconstructed by single-pixel imaging technology fails to match traditional cameras. Since it requires a sequence of measurements to retrieve a single image, the temporal fluctuation of illumination intensity during the measuring will cause inconsistence for consecutive measurements and thus noise in reconstructed images. In this paper, a normalization protocol utilizing the differential measurements in single-pixel imaging is proposed to reduce such inconsistence with no additional hardware required. Numerical and practical experiments are performed to investigate the influences of temporal fluctuation of different degrees on image quality and to demonstrate the feasibility of the proposed normalization protocol. Experimental results show that our normalization protocol can match the performance of the system with the reference arm. The proposed normalization protocol is straightforward with the potential to be easily applied in any temporal-sequence imaging strategy. [ABSTRACT FROM AUTHOR]

Let $Q_n=[0,1]^n$ be the unit cube in ${\mathbb R}^n$ and let $C(Q_n)$ be a space of continuous functions $f:Q_n\to{\mathbb R}$ with the norm $\|f\|_{C(Q_n)}:=\max_{x\in Q_n}|f(x)|.$ By $\Pi_1\left({\mathbb R}^n\right)$ denote a set of polynomials in $n$ variables of degree $\leq 1$, i. e., a set of linear functions on ${\mathbb R}^n$. The interpolation projector $P:C(Q_n)\to \Pi_1({\mathbb R}^n)$ with the nodes $x^{(j)}\in Q_n$ is defined by the equalities $Pf\left(x^{(j)}\right)= f\left(x^{(j)}\right)$, $j=1,$ $\ldots,$ $ n+1$. Let $\|P\|_{Q_n}$ be the norm of $P$ as an operator from $C(Q_n)$ to $C(Q_n)$. If $n+1$ is an Hadamard number, then there exists a non-degenerate regular simplex having the vertices at vertices of $Q_n$. We discuss some approaches to get inequalities of the form $||P||_{Q_n}\leq c\sqrt{n}$ for the norm of the corresponding projector $P$.

• Hybrid transforms are integrated in computational ghost imaging to simplify image reconstruction. • In experiments, hybridizations of Hadamard, discrete cosine, and Haar transform matrices are exploited. • With hybrid transforms, computational ghost imaging makes image encoding and image compression conveniently. • Computational ghost imaging with hybrid transforms may find flexible applications in image processing. A scenario of ghost imaging with hybrid transform approach is proposed by integrating Hadamard, discrete cosine, and Haar matrices. The measurement matrix is formed by the Kronecker product of the two different transform matrices. The image information can be conveniently reconstructed with the corresponding inverse matrices. In experiment, six sets of transform hybridizations are performed in computational ghost imaging. For an object of staggered stripes, only one bucket signal survives in the Hadamard-cosine, Haar-Hadamard, and Haar-cosine hybridization sets, showing flexible image compression. For a handmade windmill object, the quality factors of the reconstructed images vary with the hybridization sets. Sub-Nyquist sampling can be applied to either or both of the different transform matrices in each hybridization set in experiment. The hybridization method can be extended to apply more transforms in one experiment. Ghost imaging with hybrid transforms may find flexible applications in image processing, such as image compression and image encryption. [ABSTRACT FROM AUTHOR]

Computational ghost imaging, as an alternative photoelectric imaging technology, uses a single-pixel detector with no spatial resolution to capture information and reconstruct the image of a scene. Due to its essentially temporal measurement manner, improving the image frame rate is always a major concern in the research of computational ghost imaging technology. By taking advantage of the fast switching time of LED, an LED array was developed to provide a structured illumination light source in our work, which significantly improves the structured illumination rate in the computational ghost imaging system. The design of the LED array driver circuit presented in this work makes full use of the LED switching time and achieves a pattern displaying rate of 12.5 MHz. Continuous images with 32 × 32 pixel resolution are reconstructed at a frame rate of 25,000 fps, which is approximately 500 times faster than what a universally used digital micromirror device can achieve. The LED array presented in this work can potentially be applied to other techniques requiring high-speed structured illumination, such as fringe 3D profiling and array-based LIFI.

The existing approach for evaluating the statistical characteristics of speckle intensity distribution is applicable only to completely decorrelated laser beams. In the current study, a theoretical method based on a coherent matrix is developed for evaluating the first-order speckle statistics of partially correlated beams. A rigorous analytical formula for the calculation of speckle contrast is obtained based on the proposed coherent matrix method. Subsequently, an approximate analysis model of the speckle intensity distribution in a laser spot illuminated by partially correlated beams is proposed. The simulation results show that the accuracy of the approximate analysis model increases with the number of beams and is acceptable for practical application, even for a small number of beams. Applications of the proposed method are presented for analyzing two different optical schemes for speckle suppression. It is shown that the developed theoretical method is straightforward and effective for the analysis of light intensity statistics of laser spots illuminated by partially correlated beams. Therefore, the developed method can be easily generalized to imaging systems with partially correlated laser beams for evaluating the speckle intensity statistics.

This note presents an alternative to multiple imputation and other approaches to regression analysis in the presence of missing covariate data. Our recommendation, based on factorial and fractional factorial arrangements, is more faithful to ancillarity considerations of regression analysis and involves assessing the sensitivity of inference on each regression parameter to missingness in each of the explanatory variables. The ideas are illustrated on a medical example concerned with the success of hematopoietic stem cell transplantation in children, and on a sociological example concerned with socio-economic inequalities in educational attainment.

We give explicit constructions of square (1 , − 1) -matrices of order congruent to 2 modulo 4 with large determinants. In particular, we construct nine families of near-Hadamard matrices based on almost supplementary difference sets with two blocks, and compute their determinants. As consequences, we obtain many (1 , − 1) -matrices which are almost D -optimal or have at least 80% D -efficiency. [ABSTRACT FROM AUTHOR]

Hashing plays an important role in information retrieval, due to its low storage and high speed of processing. As an effective multi-modal representation learning method, multi-modal hashing has received particular attention. Most of the existing multi-modal hashing methods adopt the fixed weighting factors to fuse multiple modalities for any query data, which cannot capture the variation among different queries. Besides, there are too much hyper-parameters in their models while it is time-consuming and labor-intensive to determine the proper parameters. The limitations may significantly hinder their promotion in practical applications. In this paper, we propose a simple, yet effective method that is inspired by the Hadamard matrix. On the one hand, our proposed method that involves a very few hyper-parameters is flexible. On the other hand, the complementary information between multi-modal data and the semantic discrimination information are preserved well in the hash codes. Extensive experimental results on four benchmark datasets show that the proposed framework is effective and achieves superior performance compared to state-of-the-art methods. [ABSTRACT FROM AUTHOR]

We discuss various results on Sidon-type inequalities and on the space of quasi-continuous functions. [ABSTRACT FROM AUTHOR]

It is proved that a code L(q) which is monomially equivalent to the Pless symmetry code C(q) of length 2 q + 2 contains the (0,1)-incidence matrix of a Hadamard 3- (2 q + 2 , q + 1 , (q - 1) / 2) design D(q) associated with a Paley–Hadamard matrix of type II. Similarly, any ternary extended quadratic residue code contains the incidence matrix of a Hadamard 3-design associated with a Paley–Hadamard matrix of type I. If q = 5 , 11 , 17 , 23 , then the full permutation automorphism group of L(q) coincides with the full automorphism group of D(q), and a similar result holds for the ternary extended quadratic residue codes of lengths 24 and 48. All Hadamard matrices of order 36 formed by codewords of the Pless symmetry code C(17) are enumerated and classified up to equivalence. There are two equivalence classes of such matrices: the Paley–Hadamard matrix H of type I with a full automorphism group of order 19584, and a second regular Hadamard matrix H ′ such that the symmetric 2-(36, 15, 6) design D associated with H ′ has trivial full automorphism group, and the incidence matrix of D spans a ternary code equivalent to C(17). [ABSTRACT FROM AUTHOR]

Using a concatenated construction for -ary codes, we construct codes over in the Lee metrics which after a proper mapping to the binary alphabet (which in the case of is the well-known Gray map) become binary Hadamard codes (in particular, Hadamard matrices). Our construction allows to increase the rank and the kernel dimension of the resulting Hadamard code. Using computer search, we construct new nonequivalent Hadamard matrices of orders , , and with various fixed values of the rank and the kernel dimension in the range of possible values. It was found that in a special case, our construction coincides with the Kronecker (or Sylvester) construction and can be regarded as a version of a presently known [1] modified Sylvester construction which uses one Hadamard matrix of order and (not necessarily distinct) Hadamard matrices of order . We generalize this modified construction by proposing a more general Sylvester-type construction based on two families of (not necessarily distinct) Hadamard matrices, namely, on matrices of order and matrices of order . The resulting matrix is of order , as in the construction from [1]. [ABSTRACT FROM AUTHOR]

This paper aims to describe the methods that were used in order to construct the Hadamard matrix and its basic properties and how it is applied in Cryptography. Moreover, this matrix was used to construct a new algorithm in cryptography.

We propose a method for imaging a periodic moving/state-changed object based on computational ghost imaging with Hadamard speckle patterns and a slow bucket detector, named as PO-HCGI. In the scheme, speckle patterns are produced from a part of each row of a Hadamard matrix. Then, in each cycle, multiple speckle patterns are projected onto the periodic moving/state-changed object, and a bucket detector with a slow sampling rate records the total intensities reflected from the object as one measurement. With a series of measurements, the frames of the moving/state-changed object can be obtained directly by the second-order correlation function based on the Hadamard matrix and the corresponding bucket detector measurement results. The experimental and simulation results demonstrate the validity of the PO-HCGI. To the best of our knowledge, PO-HCGI is the first scheme that can image a fast periodic moving/state-changed object by computational ghost imaging with a slow bucket detector. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a switching for 2-designs, which defines a type of trade. We illustrate this method by applying it to some symmetric (64, 28, 12) designs, showing that the switching introduced in this paper in some cases can be applied directly to orbit matrices. In that way we obtain six new symmetric (64, 28, 12) designs. Further, we show that this type of switching (of trades) can be applied to any symmetric design related to a Bush-type Hadamard matrix and construct symmetric designs with parameters (36, 15, 6) leading to new Bush-type Hadamard matrices of order 36, and symmetric (100, 45, 20) designs yielding Bush-type Hadamard matrices of order 100. [ABSTRACT FROM AUTHOR]

The orthogonal array holds significant importance as a research topic within the realms of combinatorial design theory and experimental design theory, with widespread applications in statistics, computer science, coding theory and cryptography. This paper presents three constructions for asymmetric orthogonal arrays including juxtaposition, generator matrices over Galois fields and mixed difference matrices. Subsequently, many new infinite families of asymmetric orthogonal arrays with strength t ≥ 3 are obtained. Furthermore, some new infinite families of large sets of orthogonal arrays with mixed levels are also obtained. [ABSTRACT FROM AUTHOR]

This paper considers coherent states for the representation of Weyl commutation relations over a field of p-adic numbers. A geometric object, a lattice in vector space over a field of p-adic numbers, corresponds to the family of coherent states. It is proven that the bases of coherent states corresponding to different lattices are mutually unbiased, and that the operators defining the quantization of symplectic dynamics are Hadamard operators.

Space-filling designs that possess high separation distance are useful for computer experiments. We propose a novel method to construct high-dimensional high-separation distance designs. The construction involves taking the Kronecker product of sub-Hadamard matrices and rotation. In addition to possessing better separation distance than most existing types of space-filling designs, our newly proposed designs enjoy orthogonality and projection uniformity and are more flexible in the numbers of runs and factors than that from most algebraic constructions. From numerical results, such designs are excellent in Gaussian process emulation of high-dimensional computer experiments. An R package on design construction is available online. [ABSTRACT FROM AUTHOR]

In this paper, the properties of symbol transformations of cyclic Hadamard matrices are studied. An infinite class of (n − 1) -variable 2-resilient rotation symmetric Boolean functions are constructed, and the nonlinearity of the constructed functions is 2 n (n − 1). The crucial technique of this method is to determine a subset T ⊆ F 2 n − 1 satisfying a correspondent condition. This is a new construction of 2-resilient rotation symmetric Boolean functions via switching the supports of (n − 1) -variable rotation symmetric Boolean functions of degree one, i.e., f 0 n − 1 (x 1 , x 2 , ⋯ , x n − 1) = ⊕ i = 1 n − 1 x i , where n = 4 t. [ABSTRACT FROM AUTHOR]

The existing approach for evaluating the statistical characteristics of speckle intensity distribution is applicable only to completely decorrelated laser beams. In the current study, a theoretical method based on a coherent matrix is developed for evaluating the first-order speckle statistics of partially correlated beams. A rigorous analytical formula for the calculation of speckle contrast is obtained based on the proposed coherent matrix method. Subsequently, an approximate analysis model of the speckle intensity distribution in a laser spot illuminated by partially correlated beams is proposed. The simulation results show that the accuracy of the approximate analysis model increases with the number of beams and is acceptable for practical application, even for a small number of beams. Applications of the proposed method are presented for analyzing two different optical schemes for speckle suppression. It is shown that the developed theoretical method is straightforward and effective for the analysis of light intensity statistics of laser spots illuminated by partially correlated beams. Therefore, the developed method can be easily generalized to imaging systems with partially correlated laser beams for evaluating the speckle intensity statistics. [ABSTRACT FROM AUTHOR]

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This brief presents a high level of integration for parallel source-synchronous interfaces using Asymmetric Crosstalk Harnessed Signaling (ACHS) on 3D routing environments. ACHS is shown to successfully overcome the high noise susceptibility related to the common encoding eigenmode present in the original Crosstalk Harnessed Signaling (CHS) scheme, with a small routing overhead. In this brief, a bus design case is presented where multiple channels are wired together in a 3D routing environment by a multi-stripline stackup. CHS and ACHS performances are compared using the same routing real-estate availability; ACHS shows a far superior performance due to the absence of the common encoding mode. The best performing eigenmodes are applied to the strobe encoding to achieve very good integrity for this critical signal. [ABSTRACT FROM AUTHOR]