Related papers: Properties of Rank Metric Codes
Universal security over a network with linear network coding has been intensively studied. However, previous linear codes and code pairs used for this purpose were linear over a larger field than that used on the network, which restricts…
In this work we will present algorithms for decoding rank metric codes. First we will look at a new decoding algorithm for Gabidulin codes using the property of Dickson matrices corresponding to linearized polynomials. We will be using a…
In this article, we study polymatroids that are representable by means of linear restricted rank-metric codes, namely, by subspaces of the space of alternating, symmetric, or Hermitian square matrices endowed with the rank metric. More…
We investigate two fundamental questions intersecting coding theory and combinatorial geometry, with emphasis on their connections. These are the problem of computing the asymptotic density of MRD codes in the rank metric, and the Critical…
The weight distribution of an error correcting code is a crucial statistic in determining it's performance. One key tool for relating the weight of a code to that of it's dual is the MacWilliams Identity, first developed for the Hamming…
Linear codes with a few weights have important applications in authentication codes, secret sharing, consumer electronics, etc.. The determination of the parameters such as Hamming weight distributions and complete weight enumerators of…
In analogy with the Singleton defect for classical codes, we propose a definition of rank defect for Delsarte rank-metric codes. We characterize codes whose rank defect and dual rank defect are both zero, and prove that the rank…
Codes in the sum-rank metric have received many attentions in recent years, since they have wide applications in the multishot network coding, the space-time coding and the distributed storage. Fundamental bounds, some explicit or…
The study of the generalized Hamming weight of linear codes is a significant research topic in coding theory as it conveys the structural information of the codes and determines their performance in various applications. However,…
Security of linear ramp secret sharing schemes can be characterized by the relative generalized Hamming weights of the involved codes. In this paper we elaborate on the implication of these parameters and we devise a method to estimate…
By exploiting the connection between scattered $\mathbb{F}_q$-subspaces of $\mathbb{F}_{q^m}^3$ and minimal non degenerate $3$-dimensional rank metric codes of $\mathbb{F}_{q^m}^{n}$, $n \geq m+2$, described in [2], we will exhibit a new…
In this paper we propose a new approach to code-based signatures that makes use in particular of rank metric codes. When the classical approach consists in finding the unique preimage of a syndrome through a decoding algorithm, we propose…
In this paper, we discuss the generalized Hamming weights of a class of linear codes associated with non-degenerate quadratic forms. In order to do so, we study the quadratic forms over subspaces of finite field and obtain some interesting…
Sum-rank metric codes are a natural extension of both linear block codes and rank-metric codes. They have several applications in information theory, including multishot network coding and distributed storage systems. The aim of this…
This paper studies properties of binary runlength-limited sequences with additional constraints on their Hamming weight and/or their number of runs of identical symbols. An algebraic and a probabilistic (entropic) characterization of the…
In the recent years, the notion of rank metric in the context of coding theory has known many interesting developments in terms of applications such as space time coding, network coding or public key cryptography. These applications raised…
Minimal rank-metric codes or, equivalently, linear cutting blocking sets are characterized in terms of the second generalized rank weight, via their connection with evasiveness properties of the associated $q$-system. Using this result, we…
The sum-rank metric naturally extends both the Hamming and rank metrics in coding theory over fields. It measures the error-correcting capability of codes in multishot matrix-multiplicative channels (e.g. linear network coding or the…
The generalized Hamming weights of a linear code have been extensively studied since Wei first use them to characterize the cryptography performance of a linear code over the wire-tap channel of type II. In this paper, we investigate the…
Universal security over a network with linear network coding has been intensively studied. However, previous linear codes used for this purpose were linear over a larger field than that used on the network. In this work, we introduce new…