## WG 5: Foundational Aspects, Algebraic Methods in Random Network Coding, Distributed Storage

**Chair:** Camilla Hollanti

### Work programme

Aspects of code equivalence, distance distribution and the like are important for classification and comparison of given network codes. These are in particular applied to network codes for distributed storage. They provide powerful theoretical tools that facilitate successful work in Working Group 1 to 4. The questions are of mathematical nature and significantly impact the research field.

### Member list

Current participants list of Working Group 5 with research interests

Montserrat Alsina |
Applied Mathematics III - EPSEM Polytechnic University of Catalonia, Spain |

codes derived from algebraic structures as quaternion algebras | |

Amaro Barreal Fernandez |
Department of Mathematics and Systems Analysis Aalto University, Finland |

Distributed Storage Systems and Network Coding, Algebraic Number Theory and Applications to Coding Theory | |

Ivan Blanco-Chacon |
Department of Mathematics and Systems Analysis Aalto University, Finland |

| |

Michael Braun |
Faculty of Computer Science University of Applied Sciences Darmstadt, Germany |

Designs over GF(q), Construction of Discrete Structures in Projective Spaces, Construction of Constant Dimension Codes | |

Leo Creedon |
School of Engineering Institute of Technology Sligo, Ireland |

Algebraic code constructions, group algebras, linear block codes, algebraic number theory | |

Jan De Beule |
Department of Mathematics Ghent University, Belgium |

Finite Geometry, Coding Theory | |

Toni Ernvall |
Department of Mathematics and Statistics University of Turku, Finland |

Network Codes, Distributed Storage | |

Tuvi Etzion |
Computer Science Department Technion, Israel |

Coding Theory, Digital Sequences, Block Design | |

Thomas Feulner |
Institute for Mathematics University of Bayreuth, Germany |

Automorphism Group, Equivalence, Bounds, Construction | |

Bernat Gastón |
Information and Communications Engineering Autonomous University of Barcelona, Spain |

Distributed Storage and Computing, Information Theory | |

Marcus Greferath |
Department of Mathematics and Systems Analysis Aalto University, Finland |

Algebraic Coding Theory, q-ary Designs; Fourier inversion, Möbius inversion, Exponential sums | |

Camilla Hollanti |
Department of Mathematics and Systems Analysis Aalto University, Finland |

Distributed storage and network coding, algebraic code constructions, physical layer security, secrecy capacity of storage systems. Mathematical interests in algebraic number theory. | |

Relinde Jurrius |
Institute of Mathematics University of Neuchâtel, Switzerland |

coding theory, weight enumeration, finite geometry | |

David Karpuk |
Department of Mathematics and Systems Analysis Aalto University, Finland |

Wiretap Channels, Cryptography, Lattice Coding | |

Petteri Kaski |
Department of Information and Computer Science Aalto University, Finland |

| |

Michael Kiermaier |
Institute for Mathematics University of Bayreuth, Germany |

Codes over Rings, Finite Geometry, Computer-aided Construction of Combinatorial Objects | |

†Axel Kohnert |
Institute for Mathematics University of Bayreuth, Germany |

Construction, Classification, Bounds, Foundations | |

Mladen Kovačević |
Power, Electronics and Communication Engineering University of Novi Sad, Serbia |

Algebraic and combinatorial coding theory | |

Ivo Kubjas |
Institute of Computer Science University of Tartu, Estonia |

Index Coding | |

Jyrki Lahtonen |
Department of Mathematics University of Turku, Finland |

| |

Reinhard Laue |
Department of Computer Science/Mathematics University of Bayreuth, Germany |

t-Designs, q-Analoga of Designs | |

Daniele Manini |
Computer Science Department University of Turin, Italy |

Data replication and coded approaches in Distributed Storage Systems, Network coding for video streaming applications (P2P, CDN), Network coding application to content centric networks | |

Irene Márquez-Corbella |
Institute of Mathematics University of Valladolid, Spain |

Algebraic Coding Theory and Code-based Cryptography | |

Cristina Martínez |
Mathematics Department Autonomous University of Barcelona, Spain |

Network coding and cryptography | |

Edgar Martinez-Moro |
Institute of Mathematics University of Valladolid, Spain |

Computer-aided Construction of Representations of Codes, Codes over Rings, Group Codes | |

Aleksandar Minja |
Power, Electronics and Communication Engineering University of Novi Sad, Serbia |

Network Coding, Distributed Storage, Code Design | |

Diego Napp |
Department of Systems Engineering and Automation University of Valladolid, Spain |

Systems Theory, Convolutional Codes | |

Alejandro Nicolas |
Institute of Mathematics University of Valladolid, Spain |

Codes over Rings | |

Nicolas Normand |
IRCCyN UMR 6597 Nantes University, France |

Tomography-based Erasure Coding | |

Patric Östergård |
Dpt. of Communications and Networking Aalto University, Finland |

Coding Theory, Combinatorial Algorithms, Design Theory | |

Ferruh Özbudak |
Institute of Applied Mathematics Middle East Technical University, Turkey |

| |

Joonas Pääkkönen |
Dpt. of Communications and Networking Aalto University, Finland |

Distributed Storage, Coding Theory | |

Mario Osvin Pavčević |
Applied Mathematics, Fac. of Electrical Eng. and Computing University of Zagreb, Croatia |

Constructions of Designs, in Particular q-Analogs of t-Designs | |

Jaume Pujol |
Information and Communications Engineering Autonomous University of Barcelona, Spain |

Information Theory, Coding Theory, Distributed Storage | |

Ago-Erik Riet |
Faculty of Mathematics and Informatics University of Tartu, Estonia |

Combinatorics, Codes over Permutations | |

Cornelia Röβing |
School of Mathematical Sciences University College Dublin, Ireland |

Discrete Geometry, Coding, Crypto | |

Stefan E. Schmidt |
Institute of Algebra, Department of Mathematics TU Dresden, Germany |

| |

Natalia Silberstein |
Computer Science Department Technion, Israel |

Coding for distributed storage systems, coding in projective spaces | |

Vitaly Skachek |
Institute of Computer Science University of Tartu, Estonia |

Network Coding, Error-Correcting Codes | |

Cedomir Stefanovic |
Department of Electronic Systems Aalborg University, Denmark |

Codes-on-graphs and random access schemes (MAC layer), Distributed coding schemes for distributed storage and data persistence (packet-level coding) | |

Milos Stojakovic |
Department of Mathematics and Informatics University of Novi Sad, Serbia |

Mathematical Aspects of Network Coding, Discrete Mathematics, Combinatorial Algorithms | |

Leo Storme |
Department of Mathematics Ghent University, Belgium |

Coding Theory Related to Finite Geometry, Designs | |

Emilio Suarez-Canedo |
Information and Communications Engineering Autonomous University of Barcelona, Spain |

Information Theory, Coding Theory, Design Theory | |

Hugues Verdure |
Department of Mathematics and Statistics University of Tromsø, Norway |

coding theory, weight enumeration, cryptography, algebraic combinatorics | |

Mercè Villanueva |
Information and Communications Engineering Autonomous University of Barcelona, Spain |

Information Theory, Coding Theory, Distributed Storage | |

Dejan Vukobratovic |
Power, Electronics and Communication Engineering University of Novi Sad, Serbia |

Network Coding, Unequal Error Protection, Network Coding for Multimedia Delivery, Network Coding for Distributed Storage | |

Alfred Wassermann |
Institute for Mathematics University of Bayreuth, Germany |

Construction of Network Codes, Isomorphisms | |

Thomas Westerbäck |
Department of Mathematics KTH Royal Institute of Technology, Sweden |

Codes over Rings, Combinatorics | |

Wolfgang Willems |
Faculty of Mathematics Otto-von-Guericke University Magdeburg, Germany |

bounds for network codes, partial spread codes |