Related papers: Binary Codes and Period-2 Orbits of Sequential Dyn…
Bernoulli convolutions are certain measures on the unit interval depending on a parameter $\beta$ between 1 and 2. In spite of their simple definition, they are not yet well understood. We study their two-dimensional density which exists by…
Kim et al. (2021) gave a method to embed a given binary $[n,k]$ code $\mathcal{C}$ $(k = 3, 4)$ into a self-orthogonal code of the shortest length which has the same dimension $k$ and minimum distance $d' \ge d(\mathcal{C})$. We extend this…
Flag codes generalize constant dimension codes by considering sequences of nested subspaces with prescribed dimensions as codewords. A comprehensive construction, which unites cyclic orbit flag codes, yields two families of flag codes on…
Let $-1<\lambda<1$ and $f:[0,1)\to\mathbb{R}$ be a piecewise $\lambda$-affine map, that is, there exist points $0=c_0<c_1<\cdots <c_{n-1}<c_n=1$ and real numbers $b_1,\ldots,b_n$ such that $f(x)=\lambda x+b_i$ for every $x\in…
Spectroscopic orbits are computed for inner pairs in 9 hierarchical multiple systems (HIP 19639, 60845, 75663, 76816, 78163, 78416, 80448, 84789, and HD 105080) and for one simple binary HIP 61840. All subsystems are double-lined, and their…
Ensemble Density Functional Theory (EDFT) is a promising extension to Density Functional Theory (DFT) for calculating excited states. While Kohn-Sham eigenvalue differences underestimate gaps, EDFT has been shown to provide more accurate…
An identifying code in a graph is a subset of vertices having a nonempty and distinct intersection with the closed neighborhood of every vertex. We prove that the infimum density of any identifying code in $S_k$ (an infinite strip of $k$…
Dynamical behaviour of discrete dynamical systems has been investigated extensively in the past few decades. However, in several applications, long term memory plays an important role in the evolution of dynamical variables. The definition…
We investigate the dynamics of maps of the real line whose behavior on an invariant interval is close to a rational rotation on the circle. We concentrate on a specific two-parameter family, describing the dynamics arising from models in…
A code is said to be equidistant if the distance between any two distinct codewords of the code is the same. In this paper, we have studied equidistant single-orbit cyclic and quasi-cyclic subspace codes. The orbit code generated by a…
Let $S$ be the collection of quadratic polynomial maps, and degree $2$-rational maps whose automorphism groups are isomorphic to $C_2$ defined over the rational field. Assuming standard conjectures of Poonen and Manes on the period length…
The study of frequency-hopping sequences (FHSs) has been focused on the establishment of theoretical bounds for the parameters of FHSs as well as on the construction of optimal FHSs with respect to the bounds. Peng and Fan (2004) derived…
A binary code is said to be a disjunctive list-decoding $s_L$-code (LD $s_L$-code), $s \ge 2$, $L \ge 1$, if the code is identified by the incidence matrix of a family of finite sets in which the union (or disjunctive sum) of any $s$ sets…
Cyclic orbit codes are constant dimension subspace codes that arise as the orbit of a cyclic subgroup of the general linear group acting on subspaces in the given ambient space. With the aid of the largest subfield over which the given…
Symbol-pair codes are proposed to combat pair-errors in symbol-pair read channels. The minimum symbol-pair distance is of significance in determining the error-correcting capability of a symbol-pair code. Maximum distance separable (MDS)…
Let $q$ be an odd prime power. Let $f\in \mathbb{F}_q[x]$ be a polynomial having degree at least $2$, $a\in \mathbb{F}_q$, and denote by $f^n$ the $n$-th iteration of $f$. Let $\chi$ be the quadratic character of $\mathbb{F}_q$, and…
This article analyzes the periodic orbits of Syracuse dynamical systems in a novel algebraic setting: the commutative ring of graded $n$-adic integers. Within this context, this article introduces a dual-radix modular division algorithm for…
In this paper, we extend the scope of symbolic dynamics to encompass a specific class of ideal polyhedrons in the 3-dimensional hyperbolic space, marking an important step forward in the exploration of dynamical systems in non-Euclidean…
In this paper, we consider the problem of constructing optimal average-length binary codes under the constraint that each codeword must contain at most $D$ ones, where $D$ is a given input parameter. We provide an $O(n^2D)$-time complexity…
Orientable sequences of order n are infinite periodic sequences with symbols drawn from a finite alphabet of size k with the property that any particular subsequence of length n occurs at most once in a period in either direction. They were…