## Contact

Swiss National Science Foundation (SNSF)

Wildhainweg 3P.O. Box

CH-3001 Bern

Phone +41 31 308 22 22

English title | Algebraic Constructions and Decoding of Network Codes |
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Applicant | Rosenthal Joachim |

Number | 138080 |

Funding scheme | Project funding (Div. I-III) |

Research institution | Institut für Mathematik Universität Zürich |

Institution of higher education | University of Zurich - ZH |

Main discipline | Mathematics |

Start/End | 01.10.2011 - 30.09.2013 |

Approved amount | 120'000.00 |

Discipline |
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Mathematics |

Electrical Engineering |

Information Technology |

Coding Theory; Network Coding; Constant Dimension Codes; Finite Grassmann Variety

Lead |
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Lay summary |

Coding theory has emerged out of the need for better communication and has rapidly developed as a mathematical theory in strong relationship with algebra, combinatorics and algebraic geometry. Nowadays error-correcting-codes are used in everyday practical applications such as digital-storage media, wire-line and wireless networks, and satellite and deep-space communication systems. Example of simple block codes are the international standard book numbers (ISBN), the ASCII code and various encoding schemes used to identify bank accounts. Network coding theory is concerned with the encoding and transmission of information where there may be many information sources and possibly many receivers. R. Koetter and F. Kschischang identified a fundamental mathematical question which lies at the heart of network coding. This formulation seeks the construction of good subsets of the finite Grassmann variety and it is the intended plan of the proposed research to use algebraic techniques to come up with new network codes which have better throughput and efficient decoding. In the center of the mathematical interest will be the study of orbit codes, a concept introduced by the PI and his coauthors while supported by SNF grant Project no. 126948. |

Direct link to Lay Summary | Last update: 21.02.2013 |

Name | Institute |
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Publication |
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Spread decoding in extension fields |

A complete characterization of irreducible cyclic orbit codes and their Plucker embedding |

A Complete Characterization of Irreducible Cyclic Orbit Codes and their Plücker Embedding |

Cyclic Orbit Codes |

Decoding of Subspace codes, a Problem of Schubert calculus over Finite Fields |

Decoding of Subspace codes, a Problem of Schubert calculus over Finite Fields |

List Decoding of Lifted Gabidulin Codes via the Plücker Embedding |

New lower bounds for constant dimension codes |

An algebraic approach for decoding spread codes |

Decoding of convolutional codes over the erasure channel |

On Burst Error Correction and Storage Security of Noisy Data |

On conjugacy classes of subgroups of the general linear group and cyclic orbit codes |

Plücker Embedding of Cyclic Orbit Codes |

Polynomial evaluation over finite fields: new algorithms and complexity bounds |

Group / person | Country |
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Types of collaboration |
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Shannon Institute, University College Dublin | Ireland (Europe) |

- in-depth/constructive exchanges on approaches, methods or results |

Title | Type of contribution | Title of article or contribution | Date | Place | Persons involved |
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Conference on Random network codes and Designs over GF(q) | Talk given at a conference | List Decoding of Subspace Codes | 18.09.2013 | Ghent, Belgien, Belgium | Rosenthal Joachim; Marshall Kyle; Trautmann Anna-Lena; |

SIAM 2013 - Conference on Applied Algebraic Geometry | Talk given at a conference | List Decoding of Subspace Codes | 01.08.2013 | Fort Collins, Colorado, USA, United States of America | Rosenthal Joachim; Trautmann Anna-Lena; |

European Training School in Network Coding | Talk given at a conference | Schubert Calculus over Finite Fields | 04.02.2013 | Barcelona, Spanien, Spain | Rosenthal Joachim; |

Workshop on Computational Security | Talk given at a conference | The Difficulty of constructing Oneway Trapdoor Functions | 28.11.2012 | Bellaterra, Spanien, Spain | Rosenthal Joachim; |

Colloquium talk: Linear Random Network Codes, a Grassmannian Approach | Individual talk | Linear Random Network Codes, a Grassmannian Approach | 12.10.2012 | University of Wisconsin, Madison, USA, United States of America | Rosenthal Joachim; |

MTNS 2012 | Talk given at a conference | Decoding of Subspace Codes, a Problem of Schubert Calculus | 09.07.2012 | Melbourne, Australien, Australia | Rosenthal Joachim; Trautmann Anna-Lena; |

Codes and Topology | Talk given at a conference | Convolutional Codes, a Study via Duality | 31.05.2012 | Castro Urdiales, Spanien, Spain | Rosenthal Joachim; |

Title | Date | Place |
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Zurich COST Meeting - Random Network Coding and Designs over GF (q) | 20.06.2013 | Zürich, Schweiz, Switzerland |

Trends in Coding Theory 2012 | 28.10.2012 | Ascona, Schweiz, Switzerland |

Dagstuhl Seminar in Coding Theory | 13.11.2011 | Dagstuhl, Germany, Germany |

Title | Type of contribution | Date | Place | Persons involved |
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COST Action meeting | Workshop | 29.04.2012 | Initial meeting was in Brussels, Belgium | Rosenthal Joachim; |

Communication | Title | Media | Place | Year |
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Talks/events/exhibitions | Junior Euler Society Mathematik (U18) - Kryptographie | German-speaking Switzerland | 2012 |

Talks/events/exhibitions | UZH Kinderuniversität - Wie geheim ist eine Geheimschrift | German-speaking Switzerland | 2012 |

Title | Year |
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Forschungskredit der Universitaet Zuerich | 2012 |

Number | Title | Start | Funding scheme |
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149716 | Algebraic Constructions and Decoding of Subspace Codes | 01.10.2013 | Project funding (Div. I-III) |

126948 | Algebraic Constructions of Network Codes | 01.10.2009 | Project funding (Div. I-III) |

126948 | Algebraic Constructions of Network Codes | 01.10.2009 | Project funding (Div. I-III) |

149716 | Algebraic Constructions and Decoding of Subspace Codes | 01.10.2013 | Project funding (Div. I-III) |

113251 | Algebraic Constructions of Codes on Graphs | 01.10.2006 | Project funding (Div. I-III) |

144973 | Computing equipment | 01.05.2013 | R'EQUIP |

150207 | Algebraic Aspects of Linear Network Coding | 01.01.2014 | Project funding (Div. I-III) |

Coding theory has emerged out of the need for bettercommunication and has rapidly developed as a mathematical theoryin strong relationship with algebra, combinatorics and algebraicgeometry. Nowadays error-correcting-codes are used in everydaypractical applications such as digital-storage media, wire-lineand wireless networks, and satellite and deep-space communicationsystems. Example of simple block codes are the internationalstandard book numbers (ISBN), the ASCII code and various encodingschemes used to identify bank accounts.Network coding theory is concerned with the encoding andtransmission of information where there may be many informationsources and possibly many receivers. R.~K\"otter andF.~Kschischang identified a fundamental mathematicalquestion which lies at the heart of network coding. Thisformulation seeks the construction of good subsets of thefinite Grassmann variety and it is the intended plan of theproposed research to use algebraic techniques to come up with newnetwork codes which have better performance.

Swiss National Science Foundation (SNSF)

Wildhainweg 3P.O. Box

CH-3001 Bern

Phone +41 31 308 22 22

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