Related papers: Column distance of convolutional codes over Zpr
The main conjecture on maximum distance separable (MDS) codes states that, execpt for some special cases, the maximum length of a q-ary linear MDS code is q+1. This conjecture does not hold true for near maximum distance separable codes…
MDS codes have diverse practical applications in communication systems, data storage, and quantum codes due to their algebraic properties and optimal error-correcting capability. In this paper, we focus on a class of linear codes and…
In phylogenetics, distances are often used to measure the incongruence between a pair of phylogenetic trees that are reconstructed by different methods or using different regions of genome. Motivated by the maximum parsimony principle in…
In this paper, we introduce a new parameter of a code, referred to as the remoteness, which can be viewed as a dual to the covering radius. Indeed, the remoteness is the minimum radius needed for a single ball to cover all codewords. After…
We investigate punctured maximum rank distance codes in cyclic models for bilinear forms of finite vector spaces. In each of these models we consider an infinite family of linear maximum rank distance codes obtained by puncturing…
Recently, the first author together with Jens Marklof studied generalizations of the classical three distance theorem to higher dimensional toral rotations, giving upper bounds in all dimensions for the corresponding numbers of distances…
Accurate estimation of evolutionary distances between taxa is important for many phylogenetic reconstruction methods. In the case of bacteria, distances can be estimated using a range of different evolutionary models, from single nucleotide…
Goppa codes form an important class of alternant codes with wide applications in algebraic coding theory and code-based cryptography. Determining the true minimum distance of a Goppa code is a difficult problem. In this paper, we provide a…
Vector-mode geospatial data -- points, lines, and polygons -- must be encoded into an appropriate form in order to be used with traditional machine learning and artificial intelligence models. Encoding methods attempt to represent a given…
Cyclic codes are an important class of linear codes. Bounding the minimum distance of cyclic codes is a long-standing research topic in coding theory, and several well-known and basic results have been developed on this topic. Recently,…
In this paper we investigate codes over finite commutative rings R, whose generator matrices are built from \$\alpha\$-circulant matrices. For a non-trivial ideal I<R we give a method to lift such codes over R/I to codes over R, such that…
The multidimensional convolutional codes are an extension of the notion of convolutional codes (CCs) to several dimensions of time. This paper explores the class of two-dimensional convolutional codes (2D CCs) and 2D tail-biting…
This paper deals with the problem of increasing the minimum distance of a linear code by adding one or more columns to the generator matrix. Several methods to compute extensions of linear codes are presented. Many codes improving the…
We study the existence over small fields of Maximum Distance Separable (MDS) codes with generator matrices having specified supports (i.e. having specified locations of zero entries). This problem unifies and simplifies the problems posed…
In this paper, the extremal graph with the maximum RRD-value among all the graphs of order n with given cut vertices or edges is characterized. In addition, an upper bounds on the reciprocal degree distance in terms of the number of cut…
It is proved that for any finite dimensional representation of a prime order group over the field of rational numbers, polynomial invariants of degree at most $3$ separate the orbits. A result providing an upper degree bound for separating…
We consider linear cyclic codes with the locality property, or locally recoverable codes (LRC codes). A family of LRC codes that generalize the classical construction of Reed-Solomon codes was constructed in a recent paper by I. Tamo and A.…
The Etzion-Silberstein conjecture asserts that, for any finite field $\mathbb F$, Ferrers diagram $\mathcal D$, and integer $d$, there exists a linear matrix code supported on $\mathcal D$ with minimum rank distance $d$ that attains a…
Recent work has shown that properly designed protograph-based LDPC codes may have minimum distance linearly increasing with block length. This notion rests on ensemble arguments over all possible expansions of the base protograph. When…
In this paper, we propose two novel modulation concepts based on a simple maximum distance separable (MDS) code { and show that these concepts can achieve better error performance than index modulation (IM) and related schemes.} In the…