Related papers: On Construction of Hadamard Matrices
Hadamard ideals were introduced in 2006 as a set of nonlinear polynomial equations whose zeros are uniquely related to Hadamard matrices with one or two circulant cores of a given order. Based on this idea, the cocyclic Hadamard test enable…
This paper examines the structure of poset matrices by formulating a set of new construction rules for this purpose. In this direction, the technique of partial composition operation will be introduced as the basis for the construction of…
We construct a series HMT$(n)$ of $2$-dimensional simplicial complexes with torsion $H_1($HMT$(n))=(\mathbb{Z}_2)^{{k}\choose{1}} \times (\mathbb{Z}_4)^{{k}\choose{2}} \times \cdots \times (\mathbb{Z}_{2^k})^{{k}\choose{k}}$,…
Time series classification holds broad application value in communications, information countermeasures, finance, and medicine. However, state-of-the-art (SOTA) methods-including HIVE-COTE, Proximity Forest, and TS-CHIEF-exhibit high…
In this study, the author establish some inequalities of Hadamard like based on convex and s-convexity in the second sense. Some applications to special means of positive real numbers are also given.
In this paper we construct exponentionally many non-isomorphic skew Hadamard difference sets over an elementary abelian group of order $q^3$.
The generators of the classical Specht module satisfy intricate relations. We introduce the Specht matroid, which keeps track of these relations, and the Specht polytope, which also keeps track of convexity relations. We establish basic…
Matrices with the structures of Toeplitz, Hankel, Vandermonde and Cauchy types are omnipresent in modern computation. The four classes have distinct features, but in 1990 we showed that Vandermonde and Hankel multipliers transform all these…
We introduce numerical characteristics of Sylvester and Hadamard matrices and give their estimates and some of their applications.
In this article, we consider a special class of Williamson type matrices which we call them near Williamson matrices. They are in fact four $n\times n$ $(-1, 1)$-matrices $A, B, C, D$ so that $A$ is circulant, $B,C,D$ are symmetric…
We analyze the set of real and complex Hadamard matrices with additional symmetry constrains. In particular, we link the problem of existence of maximally entangled multipartite states of $2k$ subsystems with $d$ levels each to the set of…
Hadamard matrices in $\{0,1\}$ presentation are square $m\times m$ matrices whose entries are zeros and ones and whose rows considered as vectors in $\Bbb R^m$ produce the Gram matrix of a special form with respect to the standard scalar…
We give a new characterization of skew Hadamard matrices of size $n$ in terms of the data of the spectra of tournaments of size $n-2$.
We describe properties of Hadamard products of algebraic varieties. We show any Hadamard power of a line is a linear space, and we construct star configurations from products of collinear points. Tropical geometry is used to find the degree…
The purpose of this paper is to introduce new parametric families of complex Hadamard matrices in two different ways. First, we prove that every real Hadamard matrix of order N>=4 admits an affine orbit. This settles a recent open problem…
In this paper we introduce modular symmetric designs and use them to study the existence of Hadamard matrices modulo 5. We prove that there exist 5-modular Hadamard matrices of order n if and only if n != 3, 7 (mod 10) or n != 6, 11. In…
A three-parameter family of complex Hadamard matrices of order 6 is presented. It significantly extends the set of closed form complex Hadamard matrices of this order, and in particular contains all previously described one- and…
We construct orthogonal arrays OA$_{\lambda} (k,n)$ (of strength two) having a row that is repeated $m$ times, where $m$ is as large as possible. In particular, we consider OAs where the ratio $m / \lambda$ is as large as possible; these…
This work provides explicit characterizations and formulae for the minimal polynomials of a wide variety of structured $4\times 4$ matrices. These include symmetric, Hamiltonian and orthogonal matrices. Applications such as the complete…
All generalized Hadamard matrices of order 18 over a group of order 3, H(6,3), are enumerated in two different ways: once, as class regular symmetric (6,3)-nets, or symmetric transversal designs on 54 points and 54 blocks with a group of…