## WG 4: Construction of Network Codes and Grassmannian Codes

**Chairs:** Tuvi Etzion, Joachim Rosenthal

### Work programme

Traditional coding theory is aware of two different construction issues, one of them a purely practical, where the other being more theoretical and particularly touching asymptotic aspects of coding. The former type of construction is interested in codes of small size and small length that come with efficient encoders and decoders and are ready for implementation in communication devices. The latter focuses on the existence of infinite families of codes for which information rate and error-correction capabilities are clearly bounded away from zero. Particularly in search of good network codes of relatively small size in small projective geometries intelligent searches based on assumptions on the inner symmetry of the code can significantly help the construction process. This task is of highly mathematical nature and requires strong computational power for the resulting searches. Judging the quality of its outcomes will require results from Working Group 1.

**Survey with open problems**

- T. Etzion.
*Problems on q-Analogs in Coding Theory.*arXiv

### Member list

Current participants list of Working Group 4 with research interests

Paulo Almeida |
Department of Mathematics University of Aveiro, Portugal |

Convolutional codes, finite fields, superregular matrices, subspace codes | |

Christine Bachoc |
Bordeaux Institute of Mathematics University of Bordeaux, France |

Bounds and Constructions of Network Codes | |

Daniele Bartoli |
Department of Mathematics Ghent University, Belgium |

Coding Theory, Algebraic Codes, Functional Codes | |

Simon Blackburn |
Mathematics Department Royal Holloway, University of London, UK |

Combinatorics, Coding Theory, Cryptography | |

Sarit Buzaglo |
Computer Science Department (–14) Technion, Israel |

Algebraic Coding Theory, Error-Correcting Codes for Non-Volatile Memories, Discrete Geometry and Combinatorics | |

Eimear Byrne |
School of Mathematics and Statistics University College Dublin, Ireland |

Codes over Rings, Decoding Algorithms, Network Coding, Codes and Combinatorial Structures | |

Ilaria Cardinali |
Department of Information Engineering and Mathematics University of Siena, Italy |

Polar Grassmannians, Grassmann Codes, Projective Linear Codes | |

Joan-Josep Climent |
Department of Statistics and Operations Research University of Alicante, Spain |

Linear Algebra, Coding Theory, Cryptography | |

Sara Díaz Cardell |
Department of Statistics and Operations Research (–15) University of Alicante, Spain |

Coding Theory, Cryptology, Computational Security, Network Coding | |

Andreas-Stephan Elsenhans |
Institute of Mathematics University of Paderborn, Germany |

| |

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 | |

Szabolcs Levente Fancsali |
Institute of Mathematics Eötvös Loránd University, Hungary |

Finite geometry (t-spreads); Network coding and secret sharing | |

Thomas Feulner |
Institute for Mathematics (–13) University of Bayreuth, Germany |

Automorphism Group, Equivalence, Bounds, Construction | |

Olav Geil |
Department of Mathematical Sciences Aalborg University, Denmark |

Algebraic Coding Theory, Network Coding and Polynomials over Finite Fields | |

Luca Giuzzi |
DICATAM - Section of Mathematics University of Brescia, Italy |

Coding theory; Cryptography; Finite Geometry | |

Faruk Gologlu |
Claude Shannon Institute University College Dublin, Ireland |

Finite Fields, Polynomials over Finite Fields | |

Elisa Gorla |
Institute of Mathematics University of Neuchâtel, Switzerland |

Network Coding, Cryptography, GrÃ¶bner Bases, Algebraic Combinatorics | |

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

Algebraic Coding Theory, q-ary Designs; Fourier inversion, MÃ¶bius inversion, Exponential sums | |

Russell Higgs |
School of Mathematical Sciences University College Dublin, Ireland |

Algebraic Coding Theory, Network Coding, Wireless Sensor Networks | |

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. | |

José Ignacio Iglesias Curto |
Department of Mathematics University of Salamanca, Spain |

Convolutional codes, algebraic geometric codes, decoding algorithms, optimal constructions | |

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 | |

Sascha Kurz |
Institute for Mathematics University of Bayreuth, Germany |

Random Network Coding, Exhaustive Search, Integer Linear Programming | |

Ivan Landjev |
Department of Informatics New Bulgarian University, Bulgaria |

Network Codes, q-Analogs of Designs, Chain Ring Analogs of Designs, Bounds for Network Codes | |

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

Network coding and cryptography | |

Umberto Martínez-Peñas |
Department of Mathematical Sciences Aalborg University, Denmark |

Algebraic Coding Theory, Network Coding, Cryptography | |

Gary McGuire |
School of Mathematics and Statistics University College Dublin, Ireland |

Algebraic Methods in Network Coding | |

José María Muñoz Porras |
Department of Mathematics University of Salamanca, Spain |

Convolutional codes, algebraic geometric codes, decoding algorithms, optimal constructions | |

Anamari Nakic |
Faculty of Electrical Engineering and Computing University of Zagreb, Croatia |

Designs over GF(q) | |

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

Coding Theory, Combinatorial Algorithms, Design Theory | |

Kamil Otal |
Institute of Applied Mathematics Middle East Technical University, Turkey |

Network Coding, AG Codes | |

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

| |

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 | |

Francesco Pavese |
Dpt. of Mathematics, Informatics and Economics University of Basilicata, Italy |

Construction of Network Codes and Grassmannian Codes, Bounds on the Size of Network Codes | |

Ruud Pellikaan |
Discrete Mathematics Technical University Eindhoven, Netherlands |

Error Correcting Codes, Algebraic Geometry Codes, Code Based Cryptography | |

Raquel Pinto |
Department of Mathematics University of Aveiro, Portugal |

Bounds on the Size of Network Codes and Construction of Network Codes and Grassmannian Codes | |

Alberto Ravagnani |
Institute of Mathematics University of Neuchâtel, Switzerland |

Network Coding | |

Netanel Raviv |
Computer Science Department Technion, Israel |

Network Coding, Subspace Codes, Designs over Finite Fields | |

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

Combinatorics, Codes over Permutations | |

Paula Rocha-Malonek |
Faculty of Engineering University of Porto, Portugal |

Foundational Aspects, Algebraic Methods in Random Network Coding; Construction of Network Codes | |

Joachim Rosenthal |
Institute of Mathematics University of Zurich, Switzerland |

Network Codes, Schubert Calculus, Convolutional Codes | |

Vanessa Santana |
Department of Mathematics University of Aveiro, Portugal |

Construction of Network Codes and Grassmannian Codes | |

Maria Conceição Santos Rocha |
Department of Mathematics University of Aveiro, Portugal |

Network coding, error-correcting codes | |

Natalia Silberstein |
Computer Science Department Technion, Israel |

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

Rita Simões |
Department of Mathematics University of Aveiro, Portugal |

| |

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

Network Coding, Error-Correcting Codes | |

Xaro Soler |
Department of Statistics and Operations Research University of Alicante, Spain |

Finite Group Theory, Network Coding | |

Eda Tekin |
Institute of Applied Mathematics Middle East Technical University, Turkey |

Network Coding, Subspace Codes | |

Marisa Toste |
School of Technology and Management Polytechnic Institute of Coimbra, Portugal |

| |

M. Ángeles Vázquez-Castro |
Telecommunications and Systems Engineering Autonomous University of Barcelona, Spain |

Network Coding for Throughput Improvement and for Reliability Improvement; Physical Layer, Network Layer | |

Paolo Vettori |
Department of Mathematics University of Aveiro, Portugal |

Construction of Network Codes and Convolutional Network Codes | |

Renata Vlahović |
Department of Mathematics University of Zagreb, Croatia |

Quasi-symmetric designs | |

Antonia Wachter-Zeh |
Institute for Communications Engineering Technical University of Munich, Germany |

Network coding, Rank metric codes (Gabidulin codes) | |

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

Construction of Network Codes, Isomorphisms | |

Alexander Zeh |
Computer Science Department (–16) Technion, Israel |

Reed-Solmon Codes, Cyclic Codes, List Decoding |