Related papers: Self-dual Hadamard bent sequences
Deep metric learning aims to learn an embedding space where the distance between data reflects their class equivalence, even when their classes are unseen during training. However, the limited number of classes available in training…
Complex Hadamard matrices have received considerable attention in the past few years due to their appearance in quantum information theory. While a complete characterization is currently available only up to order 5 (in \cite{haagerup}),…
We describe a construction of three-dimensional Hadamard matrices of even order $v$ such that $v-1$ is a prime power. The construction covers infinitely many orders for which the existence was previously open.
Base sequences BS(m,n) are quadruples (A;B;C;D) of {+1,-1}-sequences, A and B of length m and C and D of length n, the sum of whose non-periodic auto-correlation functions is zero. Base sequences and some special subclasses of BS(n+1,n)…
We study a class of holomorphic matrix models. The integrals are taken over middle dimensional cycles in the space of complex square matrices. As the size of the matrices tends to infinity, the distribution of eigenvalues is given by a…
The problem of classifying all unitary R-matrices of arbitrary finite dimension that have precisely two distinct eigenvalues is described, working up to a natural equivalence relation given by the characters of their braid group…
In this paper we provide an analytical procedure which leads to a system of $(n-2)^2$ polynomial equations whose solutions give the parameterisation of the complex $n\times n$ Hadamard matrices. It is shown that in general the Hadamard…
This paper is the first paper of three papers in a series, which intend to provide a systematic treatment for the space-filling curves of self-similar sets. In the present paper, we introduce a notion of \emph{linear graph-directed IFS}…
Commutative hypercomplex algebras offer significant advantages over traditional quaternions due to their compatibility with linear algebra techniques and efficient computational implementation, which is crucial for broad applicability. This…
In this paper, a new method is presented to compute the 2-adic complexity of pseudo-random sequences. With this method, the 2-adic complexities of all the known sequences with ideal 2-level autocorrelation are uniformly determined. Results…
The Strong Exponential Time Hypothesis (SETH) is a standard assumption in (fine-grained) parameterized complexity and many tight lower bounds are based on it. We consider a number of reasonable weakenings of the SETH, with sources from (i)…
We perform forward error analysis for a large class of recursive matrix multiplication algorithms in the spirit of [D. Bini and G. Lotti, Stability of fast algorithms for matrix multiplication, Numer. Math. 36 (1980), 63--72]. As a…
We introduce qustochastic matrices as the bistochastic matrices arising from quaternionic unitary matrices by replacing each entry with the square of its norm. This is the quaternionic analogue of the unistochastic matrices studied by…
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…
The square of a skew-symmetric matrix is a symmetric matrix whose eigenvalues have even multiplicities. When the matrices have rank two, they represent the Grassmannian of lines, and the squaring operation takes Pl\"ucker coordinates to…
In this paper we consider a problem of searching a space of predictive models for a given training data set. We propose an iterative procedure for deriving a sequence of improving models and a corresponding sequence of sets of non-linear…
In this paper the approach to obtaining nonrecurrent formulas for some recursively defined sequences is illustrated. The most interesting result in the paper is the formula for the solution of quadratic map-like recurrence. Also, some…
The defect of a complex Hadamard matrix $H$ is an upper bound for the dimension of a continuous Hadamard orbit stemming from $H$. We provide a new interpretation of the defect as the dimension of the center subspace of a gradient flow and…
This work introduces a new class of symmetric matrix structures, called harmonic structures, which enable the generation of all possible directed transitions $(x_i, x_{i+1})$ over a set of $n$ symbols, without internal repetitions. Unlike…
We study ternary sequences associated with a multidimensional continued fraction algorithm introduced by the first author. The algorithm is defined by two matrices and we show that it is measurably isomorphic to the shift on the set…