SS17 - Combinatorial and Geometrical Methods in Contemporary Coding Theory
link to the session's webpage
The theory of error-correcting codes has inspired many mathematicians who were interested in applying techniques from algebra and discrete mathematics in order to progress on questions in information processing. Coding theory lies at the intersection of several disciplines in pure and applied mathematics such as algebra, number theory, probability theory, statistics, combinatorics, complexity theory, and statistical physics, which all have helped in the past to increase our knowledge in communication theory. The design of error-correcting codes for the reliable transmission of information across noisy channels plays a crucial role in the modern era due to the massive overall communication traffic. To this aim, it has been necessary to develop sophisticated algebraic, combinatorial and geometric tools in order to construct codes that can correct as many errors as possible in a very efficient way.
This session is focused on the application of computer algebra to coding theory which, together with classical and new methods from combinatorics and geometry, can be used to obtain several and important results, such as construction of optimal codes, definition of efficient encoding and decoding algorithms and the study of algebraic, geometric and combinatorial problems arising from practical problems in coding theory. We wish to invite talks about recent results and developments in coding theory, including but not restricted to:
- Algebraic coding theory
- Rank/sum-rank metric codes
- Algebraic geometry codes
- Graph theory methods in coding theory
- Convolutional codes
- Quantum codes
- Algebraic decoding algorithms
- Combinatorial algorithms
- Computational results
- Related algebraic and combinatorial structures
Session organizers
| Gianira N. Alfarano (University of Rennes, France) |
| Giovanni Longobardi (Università degli Studi di Napoli Federico II, Italy) |
Talks
| Alessandro Neri - The geometry of one-weight linear rank-metric codes |
| Luca Bastioni - Characteristic polynomial of linearized polynomials |
| Francesco Ghiandoni - Towards the classification of scattered binomials |
| Valentina Pepe - Codes deriving from some subvarieties of the Segre variety |
| Elisa Junghans - Construction of LDPC convolutional codes from Latin squares |
| Julia Lieb - Construction of partial unit-memory MDP convolutional codes with low encoding and decoding complexity |
| Tefjol Pllaha - Quantum LDPC codes and decoding challenges |
| Michael Schaller - Lattices over Non-Archimedean Fields and Their Applications to Coding Theory |
| Valentino Smaldore - Equivalences of rank distance codes |
| Rocco Trombetti - On the minimum weight of some geometric codes |
| Cristina Fernández-Córdoba - Hamming weight distributions of linear simplex codes over finite chain rings and their Gray map |
| Carlos Vela Cabello - On some properties of the Gray map |