Floquet phases of matter have attracted great attention due to their dynamical and topological nature that are unique nonequilibrium settings. In this work, we introduce a generic way taking any integer q q th-root the evolution operator U display="inline">U describe...

We present a N-dimensional generalization of the two-dimensional block-circulant perfect array construction by [Blake, 2013]. As in [Blake, 2013], the families of N-dimensional arrays possess pairwise good zero correlation zone (ZCZ) cross-correlation. Both constructions use a perfect autocorre-lation sequence with the array orthogonality property (AOP). This paper presents a generalization of ...

Let m > 2, ζm an m-th primitive root of 1, q ≡ 1 mod 2m a prime number, s = sq a primitive root modulo q and f = fq = (q − 1)/m. We study the Jacobi sums Ja,b = − ∑q−1 k=2 ζ a inds(k)+b inds(1−k) m , 0 ≤ a, b ≤ m−1, where inds(k) is the least nonnegative integer such that s inds(k) ≡ k mod q. We exhibit a set of properties that characterize these sums, some congruences they satisfy, and a MAPLE...

Let $G = (V, E)$ be a simple graph. Denote by $D(G)$ the diagonal matrix $diag(d_1,cdots,d_n)$, where $d_i$ is the degree of vertex $i$  and  $A(G)$ the adjacency matrix of $G$. The  signless Laplacianmatrix of $G$ is $Q(G) = D(G) + A(G)$ and the $k-$th signless Laplacian spectral moment of  graph $G$ is defined as $T_k(G)=sum_{i=1}^{n}q_i^{k}$, $kgeqslant 0$, where $q_1$,$q_2$, $cdots$, $q_n$ ...

A k x k matrix A = [aU lover a field F is called circulant if aij = a (j-i) mod k' A [2k ,k l linear code over F = GF (q) is called double-circulant if it is generated by a matrix of the fonn [I A l, where A is a circulant matrix. In this work we ftrst employ the Fourier transform techJ nique to analyze and construct se:veral families of double-circulant codes. The minimum distance of the resul...

An r × r matrix A = [aij] over a field F is called circulant if aij = a0, ( j−i) mod r . An [n = 2r, k = r] linear code over F = GF(q) is called double-circulant if it is generated by a matrix of the form [I A], where A is an r × r circulant matrix. In this work we first employ the Fourier transform technique to analyze and construct several families of double-circulant codes. The minimum dista...

The goal of this paper is two-fold. We first focus on the problem of deciding whether two monomial rotation symmetric (MRS) Boolean functions are affine equivalent via a permutation. Using a correspondence between such functions and circulant matrices, we give a simple necessary and sufficient condition. We connect this problem with the well known Ádám’s conjecture from graph theory. As applica...

The present paper deals with the complexity of computation of a sequence of Boolean matrices via universal commutative additive circuits, i.e. circuits of binary additions over the group (Z, +) (an additive circuit implementing a matrix over (Z, +), implements the same matrix over any commutative semigroup (S, +).) Basic notions of circuit and complexity see in [3, 5]. Denote the complexity of ...

let $g = (v, e)$ be a simple graph. denote by $d(g)$ the diagonal matrix $diag(d_1,cdots,d_n)$, where $d_i$ is the degree of vertex $i$  and  $a(g)$ the adjacency matrix of $g$. the  signless laplacianmatrix of $g$ is $q(g) = d(g) + a(g)$ and the $k-$th signless laplacian spectral moment of  graph $g$ is defined as $t_k(g)=sum_{i=1}^{n}q_i^{k}$, $kgeqslant 0$, where $q_1$,$q_2$, $cdots$, $q_n$ ...