Related papers: A complex Hadamard matrix of order 94

In this paper it is proved, that for every prime number p, the set of cyclic p-roots in C^p is finite. Moreover the number of cyclic p-roots counted with multiplicity is equal to (2p-2)!/(p-1)!^2. In particular, the number of complex…

A Hadamard matrix $H$ of order $n$ is a square matrix with entries $\pm 1$ satisfying $HH^T = nI_n$, where $I_n$ is the identity matrix of order $n$. A circulant Hadamard matrix is a Hadamard matrix whose rows are cyclic shifts of one…

A complete classification of quaternary complex Hadamard matrices of orders 10, 12 and 14 is given, and a new parametrization scheme for obtaining new examples of affine parametric families of complex Hadamard matrices is provided. On the…

In this paper we disprove the Haagerup statement that all complex Hadamard matrices of order five are equivalent with the Fourier matrix $F_5$ by constructing circulant matrices that lead to new Hadamard matrices. An important item is the…

In this article, a series of Hadamard matrix has been developed using some block matrices with the help of skew Hadamard matrix. Basically an internal structure of skew Hadamard matrix has been changed with some block matrices using…

We show that 138 odd values of n less than 10000 for which one knows how to construct a Hadamard matrix of order 4n have been overlooked in the recent handbook of combinatorial designs. There are four additional odd n, namely 191, 5767,…

We describe combinatorial properties of the defining row of a circulant Hadamard matrix by exploiting its orthogonality to subsequent rows, and show how to exclude several particular forms of these matrices.

Hadamard matrices are $(-1, +1)$ square matrices with mutually orthogonal rows. The Hadamard conjecture states that Hadamard matrices of order $n$ exist whenever $n$ is $1$, $2$, or a multiple of $4$. However, no construction is known that…

In this paper, we obtain a number of new infinite families of Hadamard matrices. Our constructions are based on four new constructions of difference families with four or eight blocks. By applying the Wallis-Whiteman array or the Kharaghani…

We construct new symmetric Hadamard matrices of orders $92,116$, and $172$. While the existence of those of order $92$ was known since 1978, the orders $116$ and $172$ are new. Our construction is based on a recent new combinatorial array…

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…

First examples of symmetric Hadamard matrices of orders 508 and 764 are constructed. The method used is known as the propus construction. A conjecture regarding this method is formally proposed but it appears implicitly in three previous…

We study the circulant complex Hadamard matrices of order $n$ whose entries are $l$-th roots of unity. For $n=l$ prime we prove that the only such matrix, up to equivalence, is the Fourier matrix, while for $n=p+q,l=pq$ with $p,q$ distinct…

A complex Hadamard matrix is a square matrix H with complex entries of absolute value 1 satisfying $HH^*= nI$, where $*$ stands for the Hermitian transpose and I is the identity matrix of order $n$. In this paper, we first determine the…

We have extended the Paley constructions for Hadamard matrices and obtained some series of Hadamard matrices. Especially Paley construction-II is applicable for odd prime power q is congruent to 1(mod 4) however our method is applicable for…

We construct several difference families on cyclic groups of orders 47 and 97, and use them to construct skew-Hadamard matrices of orders 188 and 388. Such difference families and matrices are constructed here for the first time. The…

We construct many symmetric Hadamard matrices of small order by using the so called propus construction. The necessary difference families are constructed by restricting the search to the families which admit a nontrivial multiplier. Our…

The intended purpose of this work is to provide the reader with a comprehensive, state-of-the art presentation of the theory of complex Hadamard matrices, or at least report on the very recent advances. This manuscript consists of three…

We study the existence and construction of circulant matrices $C$ of order $n\geq2$ with diagonal entries $d\geq0$, off-diagonal entries $\pm1$ and mutually orthogonal rows. These matrices generalize circulant conference ($d=0$) and…

Balancedly splittable Hadamard matrices are introduced and studied. A connection is made to the Hadamard diagonalizable strongly regular graphs, maximal equiangular lines set, and unbiased Hadamard matrices. Several construction methods are…