Related papers: Decreasing norm-trace codes
The purpose of the present article is the study of duals of functional codes on algebraic surfaces. We give a direct geometrical description of them, using differentials. Even if this geometrical description is less trivial, it can be…
An expander code is a binary linear code whose parity-check matrix is the bi-adjacency matrix of a bipartite expander graph. We provide a new formula for the minimum distance of such codes. We also provide a new proof of the result that…
Optimization over trained machine learning models has applications including: verification, minimizing neural acquisition functions, and integrating a trained surrogate into a larger decision-making problem. This paper formulates and solves…
We shall derive conditions in which a general formula for the dimension of q-ary trace codes induced by algebraic-geometric codes. Significant to this result are several dimension reducing methods for the underlying functions spaces…
Many privacy-type properties of security protocols can be modelled using trace equivalence properties in suitable process algebras. It has been shown that such properties can be decided for interesting classes of finite processes (i.e.,…
It is well known that the minimum distance for linear network codes plays the same role as the minimum distance for classical error control codes. However, Yang and Yeung (2008) discovered that for nonlinear network codes, the minimum…
This paper investigates properties of realizations of linear or group codes on general graphs that lead to local reducibility. Trimness and properness are dual properties of constraint codes. A linear or group realization with a constraint…
Classes of graphs with bounded expansion are a generalization of both proper minor closed classes and degree bounded classes. Such classes are based on a new invariant, the greatest reduced average density (grad) of G with rank r,…
Given a hypergraph $\mathcal{H}$, we introduce a new class of evaluation toric codes called edge codes derived from $\mathcal{H}$. We analyze these codes, focusing on determining their basic parameters. We provide estimations for the…
We consider the problem of estimating a time-varying sparse precision matrix, which is assumed to evolve in a piece-wise constant manner. Building upon the Group Fused LASSO and LASSO penalty functions, we estimate both the network…
The paper addresses the problem of low-rank trace norm minimization. We propose an algorithm that alternates between fixed-rank optimization and rank-one updates. The fixed-rank optimization is characterized by an efficient factorization…
We study the convergence of the Regularized Alternating Least-Squares algorithm for tensor decompositions. As a main result, we have shown that given the existence of critical points of the Alternating Least-Squares method, the limit points…
Many quantum technologies are now reaching a high level of maturity and control, and it is likely that the first demonstrations of suppression of naturally occurring quantum noise using small topological error correcting codes will soon be…
Codes considered as structures within unit schemes greatly extends the availability of linear block and convolutional codes and allows the construction of these codes to required length, rate, distance and type. Properties of a code emanate…
Labeling of DNA molecules is a fundamental technique for DNA visualization and analysis. This process was mathematically modeled in [1], where the received sequence indicates the positions of the used labels. In this work, we develop error…
In this paper we will estimate the main parameters of some evaluation codes which are known as projective parameterized codes. We will find the length of these codes and we will give a formula for the dimension in terms of the Hilbert…
A maximum distance separable (MDS) array code is composed of $m\times (k+r)$ arrays such that any $k$ out of $k+r$ columns suffice to retrieve all the information symbols. Expanded-Blaum-Roth (EBR) codes and Expanded-Independent-Parity…
We reformulate a recently introduced interpolation-based unique decoding algorithm of algebraic geometry codes using the theory of Gr\"obner bases of modules on the coordinate ring of the base curve. With the same decoding performance, the…
In this letter, locally recoverable codes with maximal recoverability are studied with a focus on identifying the MDS codes resulting from puncturing and shortening. By using matroid theory and the relation between MDS codes and uniform…
Can one reduce the size of a graph without significantly altering its basic properties? The graph reduction problem is hereby approached from the perspective of restricted spectral approximation, a modification of the spectral similarity…