Related papers: Characteristic-Dependent Linear Rank Inequalities …
We study the use of linear codes for network computing in single-receiver networks with various classes of target functions of the source messages. Such classes include reducible, injective, semi-injective, and linear target functions over…
Studying the generalized Hamming weights of linear codes is a significant research area within coding theory, as it provides valuable structural information about the codes and plays a crucial role in determining their performance in…
A combinatorial framework for adversarial network coding is presented. Channels are described by specifying the possible actions that one or more (possibly coordinated) adversaries may take. Upper bounds on three notions of capacity (the…
The minimal set of Shannon-type inequalities (referred to as elemental inequalities), plays a central role in determining whether a given inequality is Shannon-type. Often, there arises a situation where one needs to check whether a given…
Multi-antenna coded caching (CC) techniques are considered viable options for achieving higher data rates in future networks, especially for the prominent use case of multimedia-driven applications. However, despite their…
This note contains two new observations on the linkage properties of quaternion algebras over fields of characteristic 2: first, that a 3-linked field need not be 4-linked (a case which was left open in previous papers) and that three…
The present work deals with the characterization of parity vectors of Collatz sequences (of finite and infinite length). Such a characterization leads to the determination of several numbers (integers or non-integers) that we call the…
We consider the network constraints on the bounds of the assortativity coefficient, which measures the tendency of nodes with the same attribute values to be interconnected. The assortativity coefficient is the Pearson's correlation…
The linear deterministic model has been used recently to get a first order understanding of many wireless communication network problems. In many of these cases, it has been pointed out that the capacity regions of the network and its…
Identifiability of parameters is an essential property for a statistical model to be useful in most settings. However, establishing parameter identifiability for Bayesian networks with hidden variables remains challenging. In the context of…
Matrix concentration inequalities give bounds for the spectral-norm deviation of a random matrix from its expected value. These results have a weak dimensional dependence that is sometimes, but not always, necessary. This paper identifies…
In this note we reproduce Johnson's analysis of $W_2$-topologies on fields of characteristic 2, which was originally stated for fields of characteristic different than 2. Following his framework, we prove that the canonical topology of an…
In this paper we consider the dyadic effect introduced in complex networks when nodes are distinguished by a binary characteristic. Under these circumstances two independent parameters, namely dyadicity and heterophilicity, are able to…
Linear codes play a central role in coding theory and have applications in several branches of mathematics. For error correction purposes the minimum Hamming distance should be as large as possible. Linear codes related to applications in…
The multiplicative-additive finite-field matrix channel arises as an adequate model for linear network coding systems when links are subject to errors and erasures, and both the network topology and the network code are unknown. In a…
The article continues the work on the description of integrable nonlinear chains with three independent variables of the following form $u^j_{n+1,x}=u^j_{n,x}+f(u^{j+1}_{n}, u^{j}_n,u^j_{n+1 },u^{j-1}_{n+1})$ by the presence of a hierarchy…
Randomized network coding (RNC) greatly reduces the complexity of implementing network coding in large-scale, heterogeneous networks. This paper examines two tradeoffs in applying RNC: The first studies how the performance of RNC varies…
The rank decoding problem has been the subject of much attention in this last decade. This problem, which is at the base of the security of public-key cryptosystems based on rank metric codes, is traditionally studied over finite fields.…
Neural network properties are considered in the case of the interconnection tensor rank being higher than two. This sort of interconnection tensor occurs in realization of crossbar-based neural networks. It is intrinsic for a crossbar…
A (q,k,t)-design matrix is an m x n matrix whose pattern of zeros/non-zeros satisfies the following design-like condition: each row has at most q non-zeros, each column has at least k non-zeros and the supports of every two columns…