Related papers: On continuing codes
It is shown that if an infinite synchronized system has a flip, then it has infinitely many non-conjugate flips, and that the result cannot be extended to the class of coded systems.
Let $S=\{s_i\in\mathbb N\cup\{0\}:0\leq s_i<s_{i+1}\}$ and let $d_{0}=s_{0}$ and $\Delta(S)=\{d_{n}\}_{n}$ where $d_{n}=s_{n}-s_{n-1}$. In this note, we show that an $S$-gap shift is subshift of finite type (SFT) if and only if $S$ is…
Constacyclic codes over finite fields are a family of linear codes and contain cyclic codes as a subclass. Constacyclic codes are related to many areas of mathematics and outperform cyclic codes in several aspects. Hence, constacyclic codes…
Motivated by the intermediate Lang conjectures on hyperbolicity and rational points, we prove new finiteness results for non-constant morphisms from a fixed variety to a fixed variety defined over a number field by applying Faltings's…
We obtain sufficient conditions under which the limit of a sequence of functions exhibits a particular dynamical behaviour at a point like expansivity, shadowing, mixing, sensitivity and transitivity. We provide examples to show that the…
We address the recently suggested problem of causal lossless coding of a randomly arriving source samples. We construct variable-to-fixed coding schemes and show that they outperform the previously considered fixed-to-variable schemes when…
Constacyclic codes over finite fields are of theoretical importance as they are closely related to a number of areas of mathematics such as algebra, algebraic geometry, graph theory, combinatorial designs and number theory. However, the…
Concurrent coding is an unconventional encoding technique that simultaneously provides protection against noise, burst errors and interference. This simple-to-understand concept is investigated by distinguishing 2 types of code, open and…
We call a function $f: X\to Y$ $P$-preserving if, for every subspace $A \subset X$ with property $P$, its image $f(A)$ also has property $P$. Of course, all continuous maps are both compactness- and connectedness-preserving and the natural…
We study topological factors of rank-one subshifts and prove that those factors that are themselves subshifts are either finite or isomorphic to the original rank-one subshifts. Thus, we completely characterize the subshift factors of…
Block coordinate descent is an optimization paradigm that iteratively updates one block of variables at a time, making it quite amenable to big data applications due to its scalability and performance. Its convergence behavior has been…
For each type of number, structures that differ by arbitrary scaling factors and are isomorphic to one another are described. The scaling of number values in one structure, relative to the values in another structure, must be compensated…
For a flexible labeling of a graph, it is possible to construct infinitely many non-equivalent realizations keeping the distances of connected points constant. We give a combinatorial characterization of graphs that have flexible labelings.…
Shifts of finite type defined from shift equivalent matrices must be flow equivalent.
Two new classes of skew codes over a finite field $\F$ are proposed, called skew convolutional codes and skew trellis codes. These two classes are defined by, respectively, left or right sub-modules over the skew fields of fractions of skew…
We construct two new classes of topological dynamical systems; one is a factor of a one-sided shift of finite type while the second is a factor of the two-sided shift. The data is a finite graph which presents the shift of finite type, a…
The state-of-the-art error correcting codes are based on large random constructions (random graphs, random permutations, ...) and are decoded by linear-time iterative algorithms. Because of these features, they are remarkable examples of…
Number types for exact computation are usually based on directed acyclic graphs. A poor graph structure can impair the efficency of their evaluation. In such cases the performance of a number type can be drastically improved by…
We prove the property that a function is cyclic (resp., non-cyclic) is not preserved by norm convergence in Dirichlet-type spaces $D_\alpha$, and show how other significant quantities for cyclicity do remain preserved under the limit of…
We define persistent homology groups over any set of spaces which have inclusions defined so that the corresponding directed graph between the spaces is acyclic, as well as along any subgraph of this directed graph. This method…