Related papers: Topologies for Error-Detecting Variable-Length Cod…

Let A be a finite alphabet and let L contained in (A*)^n be an n-variable language over A. We say that L is regular if it is the language accepted by a synchronous n-tape finite state automaton, it is quasi-regular if it is accepted by an…

Machine-learning-based code vulnerability detection (CVD) has progressed rapidly, from deep program representations to pretrained code models and LLM-centered pipelines. Yet dependable vulnerability labeling remains expensive, noisy, and…

We consider quantum systems with a chaotic classical limit that depend on an external parameter, and study correlations between the spectra at different parameter values. In particular, we consider the parametric spectral form factor…

Building on the recent work of Mushaandja and Olela-Otafudu~\cite{MushaandjaOlela2025} on modular metric topologies, this paper investigates extended structural properties of modular (pseudo)metric spaces. We provide necessary and…

In [1], K\"otter and Kschischang presented a new model for error correcting codes in network coding. The alphabet in this model is the subspace lattice of a given vector space, a code is a subset of this lattice and the used metric on this…

We study the error detection problem in $ q $-ary asymmetric channels wherein every input symbol $ x_i $ is mapped to an output symbol $ y_i $ satisfying $ y_i \geq x_i $. A general setting is assumed where the noise vectors are…

We consider codes over the alphabet Q={0,1,..,q-1}intended for the control of unidirectional errors of level l. That is, the transmission channel is such that the received word cannot contain both a component larger than the transmitted one…

Understanding the local behaviour of structured multi-dimensional data is a fundamental problem in various areas of computer science. As the amount of data is often huge, it is desirable to obtain sublinear time algorithms, and specifically…

We study the phenomenon of mode-locking in the context of quasiperiodically forced non-linear circle maps. As a main result, we show that under certain C1-open condition on the geometry of twist parameter families of such systems, the…

If $(X,d)$ is a Polish metric space of dimension $0$, then by Wadge's lemma, no more than two Borel subsets of $X$ can be incomparable with respect to continuous reducibility. In contrast, our main result shows that for any metric space…

Topological quantum memory can protect information against local errors up to finite error thresholds. Such thresholds are usually determined based on the success of decoding algorithms rather than the intrinsic properties of the mixed…

Let $K\subset\mathbb R^d$ be a compact subset equipped with a $\delta$-Ahlfors regular measure $\mu$. For any $\tau>1/d$ and any ``inhomogeneous'' vector $\boldsymbol{\theta}\in\mathbb R^d$, let $W_d(\psi_\tau,\boldsymbol{\theta})$ denote…

Consider a $q$-ary block code satisfying the property that no $l$-letters long codeword's prefix occurs as a suffix of any codeword for $l$ inside some interval. We determine a general upper bound on the maximum size of these codes and a…

X-codes form a special class of linear maps which were originally introduced for data compression in VLSI testing and are also known to give special parity-check matrices for linear codes suitable for error-erasure channels. In the context…

We study the maximum length of $q$-ary codes as a function of alphabet size, code size, and Singleton defect. For an $(n, M, d)_q$ code with dimension $\kappa = \log_q M \ge 2$ and Singleton defect $s = n - \lceil\kappa\rceil + 1 - d$, we…

The following open problems, which concern a fundamental limit on coding properties of quantum codes with realistic physical constraints, are analyzed and partially answered here: (a) the upper bound on code distances of quantum…

We study testing of local properties in one-dimensional and multi-dimensional arrays. A property of $d$-dimensional arrays $f:[n]^d \to \Sigma$ is $k$-local if it can be defined by a family of $k \times \ldots \times k$ forbidden…

Proposed as a general framework, Liu and Yu(Discrete Math. 231 (2001) 311-320) introduced $(n,k,d)$-graphs to unify the concepts of deficiency of matchings, $n$-factor-criticality and $k$-extendability. Let $G$ be a graph and let $n,k$ and…

We consider the problem of under and over-approximating the image of general vector-valued functions over bounded sets, and apply the proposed solution to the estimation of reachable sets of uncertain non-linear discrete-time dynamical…

Codes for rank modulation have been recently proposed as a means of protecting flash memory devices from errors. We study basic coding theoretic problems for such codes, representing them as subsets of the set of permutations of $n$…