Related papers: On continuing codes

Topological behavior, such as chaos, irreducibility, and mixing of a one-sided shift of finite type, is well elucidated. Meanwhile, the investigation of multidimensional shifts, for instance, textile systems is difficult and only a few…

Semiconstrained systems were recently suggested as a generalization of constrained systems, commonly used in communication and data-storage applications that require certain offending subsequences be avoided. In an attempt to apply…

We consider a \emph{code} to be a subset of the vertex set of a \emph{Hamming graph}. In this setting a \emph{neighbour} of the code is a vertex which differs in exactly one entry from some codeword. This paper examines codes with the…

The Fischer, Krieger, and fiber product covers of sofic beta-shifts are constructed and used to show that every strictly sofic beta-shift is $2$-sofic. Flow invariants based on the covers are computed, and shown to only depend on an single…

This paper concerns non-overlapping codes, block codes motivated by synchronisation and DNA-based storage applications. Most existing constructions of these codes do not account for the restrictions posed by the physical properties of…

We introduce the notion of a contractible subshift. This is a strengthening of the notion of strong irreducibility, where we require that the gluings are given by a block map. We show that a subshift is a retract of a full shift if and only…

For a surface $S$ of sufficient complexity, Dehn twists act elliptically on the arc, curve, and relative arc graph of $S$. We show that composing a Dehn twist with a shift map results in a loxodromic isometry of the relative arc graph…

In this paper, we propose a general construction of linear perfect codes over infinite skew fields and quasi skew fields with right (left) unity. A complete classification of such codes over associative skew fields is given. Since the…

A blocks method is used to define clusters of extreme values in stationary time series. The cluster starts at the first large value in the block and ends at the last one. The block cluster measure (the point measure at clusters) encodes…

We prove that if $f:I\subset \Bbb R\to \Bbb R$ is of bounded variation, then the noncentered maximal function $Mf$ is absolutely continuous, and its derivative satisfies the sharp inequality $\|DMf\|_1\le |Df|(I)$. This allows us obtain,…

In sorting situations where the final destination of each item is known, it is natural to repeatedly choose items and place them where they belong, allowing the intervening items to shift by one to make room. (In fact, a special case of…

We define a pair of simple combinatorial operations on subshifts, called existential and universal extensions, and study their basic properties. We prove that the existential extension of a sofic shift by another sofic shift is always…

We prove a lower and an upper bound on the number of block moves necessary to sort a permutation. We put our results in contrast with existing results on sorting by block transpositions, and raise some open questions.

We define a new class of shift spaces which contains a number of classes of interest, like Sturmian shifts used in discrete geometry. We show that this class is closed under two natural transformations. The first one is called conjugacy and…

Cyclicity of a convolutional code (CC) is relying on a nontrivial automorphism of the algebra F[x]/(x^n-1), where F is a finite field. If this automorphism itself has certain specific cyclicity properties one is lead to the class of…

Computing a morph between two drawings of a graph is a classical problem in computational geometry and graph drawing. While this problem has been widely studied in the context of planar graphs, very little is known about the existence of…

We introduce a notion of coded equivalence in one-sided topological Markov shifts. The notion is inspired by coding theory. One-sided topological conjugacy implies coded equivalence. We will show that coded equivalence implies continuous…

We examine invariant nonrecurrent Fatou components of automorphisms of $\mathbb{C}^2$ in the case where all limit maps are constant. We show that except in special cases there cannot be more than one such limit map. We also briefly examine…

The problem of finding graph structure of functions commuting with a given function in terms of their functional graphs is considered. Structure of functional graphs of commuting functions is described. The problem is reduced to describing…

We investigate a variant of the chip-firing process on the infinite path graph: rather than treating the chips as indistinguishable, we label them with positive integers. To fire an unstable vertex, i.e. a vertex with more than one chip, we…