43 citations · 121 across the 14 of their papers we have counts for
20 papers
Simplex inequalities of order and chain polytopes of recursively defined posets
Ragnar Freij-Hollanti, Teemu Lundström
In this paper, we study the simplex faces of the order polytope and the chain polytope of a finite poset . We show that, if can be recursiv…
Function-Correcting Codes With Data Protection
Charul Rajput, B. Sundar Rajan, Ragnar Freij-Hollanti +1
Function-correcting codes (FCCs) are designed to provide error protection for the value of a function computed on the data. Existing work typically focuses solely on protecting the…
Two-Dimensional Faces of Order and Chain Polytopes
Ragnar Freij-Hollanti, Teemu Lundström, Aki Mori
We give an explicit combinatorial description of the two-dimensional faces of both the order polytope and the chain polytope of a partially ordere…
Matroidal Cycles and Hypergraph Families
Ragnar Freij-Hollanti, Patricija Šapokaitė
We propose a novel definition of hypergraphical matroids, defined for arbitrary hypergraphs, simultaneously generalizing previous definitions for regular hypergraphs (Main, 1978),…
-vector inequalities for order and chain polytopes
Ragnar Freij-Hollanti, Teemu Lundström
The order and chain polytopes are two 0/1-polytopes constructed from a finite poset. In this paper, we study the -vectors of these polytopes. We investigate how the order and ch…
Combinatorial Derived Matroids
Olga Kuznetsova, Ragnar Freij-Hollanti, Relinde Jurrius
Let be an arbitrary matroid with circuits . We propose a definition of a derived matroid that has as its ground set . Unlike previous attem…
Uniform Minors in Maximally Recoverable Codes
Matthias Grezet, Thomas Westerbäck, Ragnar Freij-Hollanti +1
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 matro…
Towards the Capacity of Private Information Retrieval from Coded and Colluding Servers
Lukas Holzbaur, Ragnar Freij-Hollanti, Jie Li +1
In this work, two practical concepts related to private information retrieval (PIR) are introduced and coined full support-rank PIR and strongly linear PIR. Being of full support-r…
Alphabet-Dependent Bounds for Linear Locally Repairable Codes Based on Residual Codes
Matthias Grezet, Ragnar Freij-Hollanti, Thomas Westerbäck +1
Locally repairable codes (LRCs) have gained significant interest for the design of large distributed storage systems as they allow a small number of erased nodes to be recovered by…
Private Information Retrieval from Coded Storage Systems with Colluding, Byzantine, and Unresponsive Servers
Razane Tajeddine, Oliver W. Gnilke, David Karpuk +2
The problem of Private Information Retrieval (PIR) from coded storage systems with colluding, byzantine, and unresponsive servers is considered. An explicit scheme using an …
t-Private Information Retrieval Schemes Using Transitive Codes
Ragnar Freij-Hollanti, Oliver W. Gnilke, Camilla Hollanti +3
This paper presents private information retrieval (PIR) schemes for coded storage with colluding servers, which are not restricted to maximum distance separable (MDS) codes. PIR sc…
Bounds on Binary Locally Repairable Codes Tolerating Multiple Erasures
Matthias Grezet, Ragnar Freij-Hollanti, Thomas Westerbäck +2
Recently, locally repairable codes has gained significant interest for their potential applications in distributed storage systems. However, most constructions in existence are ove…
Traffic Minimizing Caching and Latent Variable Distributions of Order Statistics
Joonas Pääkkönen, Prathapasinghe Dharmawansa, Ragnar Freij-Hollanti +2
Given a statistical model for the request frequencies and sizes of data objects in a caching system, we derive the probability density of the size of the file that accounts for the…
Matroid Theory and Storage Codes: Bounds and Constructions
Ragnar Freij-Hollanti, Camilla Hollanti, Thomas Westerbäck
Recent research on distributed storage systems (DSSs) has revealed interesting connections between matroid theory and locally repairable codes (LRCs). The goal of this chapter is t…
Private Information Retrieval Schemes for Coded Data with Arbitrary Collusion Patterns
Razane Tajeddine, Oliver W. Gnilke, David Karpuk +3
In Private Information Retrieval (PIR), one wants to download a file from a database without revealing to the database which file is being downloaded. Much attention has been paid…
A Connection Between Locally Repairable Codes and Exact Regenerating Codes
Toni Ernvall, Thomas Westerbäck, Ragnar Freij-Hollanti +1
Typically, locally repairable codes (LRCs) and regenerating codes have been studied independently of each other, and it has not been clear how the parameters of one relate to those…
Bounds on the Maximal Minimum Distance of Linear Locally Repairable Codes
Antti Pöllänen, Thomas Westerbäck, Ragnar Freij-Hollanti +1
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 f…
Applications of Polymatroid Theory to Distributed Storage Systems
Thomas Westerbäck, Ragnar Freij-Hollanti, Camilla Hollanti
In this paper, a link between polymatroid theory and locally repairable codes (LRCs) is established. The codes considered here are completely general in that they are subsets of $A…
On the Combinatorics of Locally Repairable Codes via Matroid Theory
Thomas Westerbäck, Ragnar Freij, Toni Ernvall +1
This paper provides a link between matroid theory and locally repairable codes (LRCs) that are either linear or more generally almost affine. Using this link, new results on both L…
Constructions and Properties of Linear Locally Repairable Codes
Toni Ernvall, Thomas Westerbäck, Camilla Hollanti +1
In this paper, locally repairable codes with all-symbol locality are studied. Methods to modify already existing codes are presented. Also, it is shown that with high probability,…