Related papers: Special Classes of Set Codes and Their Application…
Cyclic codes have efficient encoding and decoding algorithms over finite fields, so that they have practical applications in communication systems, consumer electronics and data storage systems. The objective of this paper is to give eight…
This article is intended as a guide for new graduate students in the field of computational science. With the increasing influx of students from diverse backgrounds joining the ever-popular field, this short guide aims to help students…
To represent anything from mathematical concepts to real-world objects, we have to resort to an encoding. Encodings, such as written language, usually assume a decoder that understands a rich shared code. A semantic embedding is a form of…
Orbit codes are a family of codes employable for communications on a random linear network coding channel. The paper focuses on the classification of these codes. We start by classifying the conjugacy classes of cyclic subgroups of the…
We construct a class of linear codes by choosing a proper defining set and determine their complete weight enumerators and weight enumerators. The results show that they are at most three-weight codes and they are suitable for applications…
A class of linear block codes which simultaneously generalizes Gabidulin codes and a class of skew cyclic codes is defined. For these codes, both a Hartmann-Tzeng-like bound and a Roos-like bound, with respect to their rank distance, are…
While functionality and correctness of code has traditionally been the main focus of computing educators, quality aspects of code are getting increasingly more attention. High-quality code contributes to the maintainability of software…
We introduce a form of steganography in the domain of machine learning which we call training set camouflage. Imagine Alice has a training set on an illicit machine learning classification task. Alice wants Bob (a machine learning system)…
In this paper, we study a security problem of protecting secrets in distributed systems. Specifically, we employ discrete-event systems to describe the structure and behaviour of distributed systems, in which global secret information is…
We consider the locality of encoding and decoding operations in distributed storage systems (DSS), and propose a new class of codes, called locally encodable and decodable codes (LEDC), that provides a higher degree of operational locality…
We describe and present a new construction method for codes using encodings from group rings. They consist primarily of two types: zero-divisor and unit-derived codes. Previous codes from group rings focused on ideals; for example cyclic…
We demonstrate propagation rules of subsystem code constructions by extending, shortening and combining given subsystem codes. Given an $[[n,k,r,d]]_q$ subsystem code, we drive new subsystem codes with parameters $[[n+1,k,r,\geq d]]_q$,…
We introduce a class of codes with overlapping code words, that we call SPO-codes. The SPO-codes are related to the Markov codes that were introduced in: G. Keller, J. Combinatorial Theory 56, (1991),pp.\ 75--83. The process of generating a…
Link and node failures are two common fundamental problems that affect operational networks. Protection of communication networks against such failures is essential for maintaining network reliability and performance. Network protection…
We propose a new class of mathematical structures called (m,n)-semirings} (which generalize the usual semirings), and describe their basic properties. We also define partial ordering, and generalize the concepts of congruence, homomorphism,…
The aim of this manuscript is to give some basic notions related to numerical semigroups, and from these on the one hand describe a classical application to the study of singularities of plane algebraic curves, and on the other, show how…
Graphs are ubiquitous in encoding relational information of real-world objects in many domains. Graph generation, whose purpose is to generate new graphs from a distribution similar to the observed graphs, has received increasing attention…
Secure coding is a critical yet often overlooked practice in software development. Despite extensive awareness efforts, real-world adoption remains inconsistent due to organizational, educational, and technical barriers. This paper provides…
We initiate the study of computational complexity of graph coverings, aka locally bijective graph homomorphisms, for {\em graphs with semi-edges}. The notion of graph covering is a discretization of coverings between surfaces or topological…
In this paper we introduce the concept of completeness of sets. We study this property on the set of integers. We examine how this property is preserved as we carry out various operations compatible with sets. We also introduce the problem…