Let H be a Hadamard matrix of order 24. In this note, we show that the extremality of the binary code of H is equivalent to the extremality of the ternary code of HT . This fact has been observed by Assmus and Key [1], as a result of the complete classification of Hadamard matrices of order 24. Our proof is a consequence of more general results on the minimum weight of the dual code of the code...

*Correspondence: [email protected]; [email protected]; [email protected] 1School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan 411105, P.R. China Full list of author information is available at the end of the article Abstract In this paper, we investigate the closure property ofH-tensors under the Hadamard product. It is shown that the Hadamard products of Had...

In this note we utilize a non-trivial block approach due to M. Petrescu to exhibit a Butson-type complex Hadamard matrix of order 19, composed of sixth roots of unity. 1 A new Butson-type complex Hadamard matrix A complex Hadamard matrix H is an n × n complex matrix with unimodular entries such that HH∗ = nIn, where ∗ denotes the Hermitian adjoint and In is the identity matrix of order n. Throu...

Hadamard matrices are useful in Hadamard transform spectroscopy and in the construction of optimal chemical designs.'-8 The use of these matrices in spectroscopy has led to the advent of Hadamard transform spectroscopy3 which employs spectroscopic multiplexing techniques and is a powerful tool for the analysis of complex spectra. Besides Hadamard matrices are useful in chemical designs and bloc...

Faculty of Arts Mathematics Department Master of Literature by Padraig Ó Catháin Hadamard matrices are an important item of study in combinatorial design theory. In this thesis, we explore the theory of cocyclic development of Hadamard matrices in terms of regular group actions on the expanded design. To this end a general theory of both group development and cocyclic development is formulated....

Say that A is a Hadamard factorization of the identity In of size n if A ◦AT = In, where ◦ denotes the Hadamard or entrywise product, and AT denotes the transpose of A. As n = rk(In) = rk(A ◦ AT ) ≤ rk(A)2, it is clear that the rank of any Hadamard factorization of the identity must be at least √ n. Dietzfelbinger et al. [DHS96] raised the question if this bound can be achieved, and showed a bo...

Hadamard speckle contrast reduction (SCR) is considered to be an effective approach to deal with speckle problems in coherent imaging systems. A Hadamard SCR system is divided into two subsystems, which implement phase patterns projection and reflected waves imaging respectively. The performances of both sub-systems are discussed with numerical simulations and linked to certain parameters so as...

This paper proposes an algorithm which can be used to construct strongly regular graphs from Hadamard matrices.A graph is strongly regular if there are integers and such that every two adjacent vertices have common neighbours and every two non adjacent vertices have common neighbors. Proposed method is mainly based on basic matrix manipulations. If the order of the normalized Hadamard matr ix i...

Hadamard conjugation can be used in the reconstruction of evolutionary trees and analysis of molecular sequence evolution. Despite the number of advantages Hadamard conjugation provides the number of evolutionary substitution models that can be used with this technique is limited. In this paper, we consider the question of whether Hadamard conjugation is limited to group-based evolutionary mode...

This paper is first study for considering nonlocal elliptic equation with Caputo derivative. We obtain the upper bound of mild solution. The second contribution to provide lower solution at terminal time. prove non-correction problem in sense Hadamard. main tool use and bounds Mittag-Lefler function, combined analysis Hilbert scales space.