相关论文: Circulant Matrix Representation of PN-sequences wi…
We calculate the autocorrelation functions (or shifted moments) of the characteristic polynomials of matrices drawn uniformly with respect to Haar measure from the groups U(N), O(2N) and USp(2N). In each case the result can be expressed in…
In this paper three Schur ring are discussed, namenly: Hamming, circulant orbists and decimated circulant orbits Schur ring. By using autocorrelation function and the run structure of binary sequences we proof the relation between this…
We introduce several new constructions for perfect periodic autocorrelation sequences and arrays over the unit quaternions. This paper uses both mathematical proofs and com- puter experiments to prove the (bounded) array constructions have…
In this paper, firstly, we give the some fundamental properties of Van Der Laan numbers. After, we define the circulant matrices C(Z) which entries is third order linear recurrent sequence. In addition, we compute eigenvalues, spectral norm…
Sequences with good correlation properties are widely used in engineering applications, especially in the area of communications. Among the known sequences, cyclotomic families have the optimal autocorrelation property. In this paper, we…
A finite sequence of numbers is perfect if it has zero periodic autocorrelation after a nontrivial cyclic shift. In this work, we study quaternionic perfect sequences having a one-to-one correspondence with the binary sequences arising in…
A family of binary sequences is presented and proved to have optimal correlation property and large linear span. It includes the small set of Kasami sequences, No sequence set and TN sequence set as special cases. An explicit lower bound…
We present a finite-order system of recurrence relations for a permanent of circulant matrices containing a band of k any-value diagonals on top of a uniform matrix (for k = 1, 2, and 3) as well as the method for deriving such recurrence…
For a restricted class of potentials (harmonic+Gaussian potentials), we express the resolvent integral for the correlation functions of simple traces of powers of complex matrices of size $N$, in term of a determinant; this determinant is…
An $m$-sequence is the one of the largest period among those produced by a linear feedback shift register. It possesses several desirable features of pseudorandomness such as balance, uniform pattern distribution and ideal autocorrelation…
The resonant transmission of a moving particle which interacts with an one-dimensional array of N delta-function potentials is investigated. A suitable transfer matrix formulation is used to obtain the particle transmission. We give the…
In this paper, we are concerned with the inversion of circulant matrices and their quantized tensor-train (QTT) structure. In particular, we show that the inverse of a complex circulant matrix $A$, generated by the first column of the form…
We consider Riordan arrays $\bigl(1/(1-t^{d+1}), ~ tp(t)\bigr)$. These are infinite lower triangular matrices determined by the formal power series $1/(1-t^{d+1})$ and a polynomial $p(t)$ of degree $d$. Columns of such matrix are eventually…
Pairs of binary sequences formed using linear combinations of multiplicative characters of finite fields are exhibited that, when compared to random sequence pairs, simultaneously achieve significantly lower mean square autocorrelation…
We calculate the autocorrelation function for the characteristic polynomial of a random matrix in the microscopic scaling regime. While results fitting this description have be proved before, we will cover all values of inverse temperature…
We study a special inhomogeneous quantum network consisting of a ring of $M$ pseudo-spins (here $M = 4$) sequentially coupled to one and the same central spin under the influence of given pulse sequences (quantum gate operations). This…
Constant amplitude zero auto-correlation (CAZAC) sequences are widely applied in waveforms for radar and communication systems. Motivated by a recent work [Berggren and Popovi\'c, IEEE Trans. Inf. Theory 70(8), 6068-6075 (2024)], this paper…
Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…
We consider the correlation functions of eigenvalues of a unidimensional chain of large random hermitian matrices. An asymptotic expression of the orthogonal polynomials allows to find new results for the correlations of eigenvalues of…
We focus on symmetries related to matrices and vectors appearing in the simulation of quantum many-body systems. Spin Hamiltonians have special matrix-symmetry properties such as persymmetry. Furthermore, the systems may exhibit physical…