Related papers: Decreasing norm-trace codes
Error-correcting codes over the real field are studied which can locate outlying computational errors when performing approximate computing of real vector--matrix multiplication on resistive crossbars. Prior work has concentrated on…
A class of random recursive sequences (Y_n) with slowly varying variances as arising for parameters of random trees or recursive algorithms leads after normalizations to degenerate limit equations of the form X\stackrel{L}{=}X. For…
The objective of this paper is to construct a class of linear codes with two nonzero weights and three nonzero weights by using the general trace functions, which weight distributions has been determined. These linear codes contain some…
Efficient computation of all distinct solutions of nonlinear problems is essential in many scientific and engineering applications. Although high-order parallel iterative schemes offer fast convergence, their practical performance is often…
We investigate the distance properties of linear locally recoverable codes (LRC codes) with all-symbol locality and availability. New upper and lower bounds on the minimum distance of such codes are derived. The upper bound is based on the…
The error coefficient of a linear code is defined as the number of minimum-weight codewords. In an additive white Gaussian noise channel, optimal linear codes with the smallest error coefficients achieve the best possible asymptotic frame…
The order statistics based list decoding techniques for linear binary block codes of small to medium block length are investigated. The construction of the list of the test error patterns is considered. The original order statistics…
A construction of expander codes is presented with the following three properties: (i) the codes lie close to the Singleton bound, (ii) they can be encoded in time complexity that is linear in their code length, and (iii) they have a…
Monotone trees - trees with a function defined on their vertices that decreases the further away from a root node one travels, are a natural model for a process that weakens the further one gets from its source. Given an aggregation of…
We use a map to quantum error-correcting codes and a subspace projection to get lower bounds for minimal homological distances in a tensor product of two chain complexes of vector spaces over a finite field. Homology groups of such a…
We define a statistical measure of the typical size of short words in a linear code over a finite field. We prove that the dual toric codes coming from polytopes of degree one are characterized, among all dual toric codes, by being extremal…
Locally repairable codes (LRCs) are error correcting codes used in distributed data storage. Besides a global level, they enable errors to be corrected locally, reducing the need for communication between storage nodes. There is a close…
Monitoring the integrity of elastic structures using ultrasonic waves requires the efficient identification of material parameters from measured surface displacements. The displacement field is governed by Cauchy's equation of motion, i.e.,…
Linear codes generated by component functions of perfect nonlinear (PN) and almost perfect nonlinear (APN) functions and the first-order Reed-Muller codes have been an object of intensive study in coding theory. The objective of this paper…
We consider an effective new method for solving trust-region and norm-regularization problems that arise as subproblems in many optimization applications. We show that the solutions to such subproblems effectively lie in a…
We give conditions under which nonuniformly expanding maps exhibit lower bounds of polynomial type for the decay of correlations and for a large class of observables. We show that if the Lasota-Yorke type inequality for the transfer…
This paper identifies and solves a new optimization problem: Given a belief network (BN) and a target ordering on its variables, how can we efficiently derive its minimal I-map whose arcs are consistent with the target ordering? We present…
An identifying code is a subset of vertices of a graph such that each vertex is uniquely determined by its neighbourhood within the identifying code. If $\M(G)$ denotes the minimum size of an identifying code of a graph $G$, it was…
We consider data transmission over a network where each edge is an erasure channel and where the inner nodes transmit a random linear combination of their incoming information. We distinguish two channel models in this setting, the row and…
This paper derives new results for the analysis of nonlinear systems by extending contraction theory in the framework of vector distances. A new tool, vector contraction analysis utilizing a notion of the vector-valued norm which evidently…