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Reed--Solomon codes are a well--studied code class which fulfill the Singleton bound with equality. However, their length is limited to the size $q$ of the underlying field $\mathbb{F}_q$. In this paper we present a code construction which…
Higher-dimensional rewriting is founded on a duality of rewrite systems and cell complexes, connecting computational mathematics to higher categories and homotopy theory: the two sides of a rewrite rule are two halves of the boundary of an…
In this paper, we mainly use classical Hermitian self-orthogonal generalized Reed-Solomon codes to construct two new classes of quantum MDS codes. Most of our quantum MDS codes have minimum distance larger than q/2+1. Compared with…
This paper is devoted to the study of sequences in overpartitions and their relation to 2-color partitions. An extensive study of a general class of double series is required to achieve these ends.
The $q$-ary block codes with two distances $d$ and $d+1$ are considered. Several constructions of such codes are given, as in the linear case all codes can be obtained by a simple modification of linear equidistant codes. Upper bounds for…
Small networks of chaotic units which are coupled by their time-delayed variables, are investigated. In spite of the time delay, the units can synchronize isochronally, i.e. without time shift. Moreover, networks can not only synchronize…
We present an explicit construction of a sequence of rate $1/2$ Wozencraft ensemble codes (over any fixed finite field $\mathbb{F}_q$) that achieve minimum distance $\Omega(\sqrt{k})$ where $k$ is the message length. The coefficients of the…
Periodic and semi periodic patterns are very common in nature. In this paper we introduce a topological toolbox aiming in detecting and quantifying periodicity. The presented technique is of a general nature and may be employed wherever…
Morphic sequences form a natural class of infinite sequences, typically defined as the coding of a fixed point of a morphism. Different morphisms and codings may yield the same morphic sequence. This paper investigates how to prove that two…
Three current models of QCD in (1+1) dimensions are examined and extended in light-front coordinates. A pion of high momentum is found to have an infinite extent along its direction of motion.
A new approach to analysis of the synchronization of chaotic oscillations in two (or more) coupled oscillators is described that makes it possible to reveal changes in the structure of attractors and detect the appearance of intermittency.…
Given a real symmetric $n\times n$ matrix, the sepr-sequence $t_1\cdots t_n$ records information about the existence of principal minors of each order that are positive, negative, or zero. This paper extends the notion of the sepr-sequence…
A known Kronecker construction of completely regular codes has been investigated taking different alphabets in the component codes. This approach is also connected with lifting constructions of completely regular codes. We obtain several…
High speed data transmission is enabled by time and wavelength division multiplexing. Here is introduced fractional dimension order of Nyquist pulses sequences for orthogonal time division multiplexing. Firstly, with a representation of the…
A new numerical characterization of symbolic sequences is proposed. The partition of sequence based on Ke and Tong algorithm is a starting point. Algorithm decomposes original sequence into set of distinct subsequences - a patterns. The set…
A linear chord diagram of size $n$ is a partition of the set $\{1,2,\cdots,2n\}$ into sets of size two, called chords. From a table showing the number of linear chord diagrams of degree $n$ such that every chord has length at least $k$, we…
Discrete time crystals (DTCs) are nonequilibrium phases of matter with exotic observable dynamics. Among their remarkable features is their response to a periodic drive at a fraction of its frequency. Current successful experiments are…
Two known 2-dim SUSY quantum mechanical constructions - the direct generalization of SUSY with first-order supercharges and Higher order SUSY with second order supercharges - are combined for a class of 2-dim quantum models, which {\it are…
We determine the isomorphism classes of Jordan algebras in dimension two over the field of real numbers. Using techniques of non-standard analysis we study the properties of the variety of Jordan algebras, and also the contractions among…
We examine combinatorial counting functions with two parameters, $n$ and $q$. For fixed $q$, these functions are (quasi-)polynomial in $n$. As $q$ varies, the degree of this polynomial is itself polynomial in $q$, as are the leading…