Since Shannon's seminal paper in 1948 the theory of communication has grown into a huge area. It encompasses different topics such as error-correcting codes, cryptography, secret sharing, steganography, source coding, network coding, and secure multiparty computation. A broad range of mathematics is involved in the study including algebra, linear algebra, computer algebra, algebraic geometry, combinatorics, and probability theory. Furthermore, many communication structures can be considered as mathematical subjects in their own right. The study of communication theory often leads to developments in purely theoretical areas which, for instance, is the case for the theory of finite fields and related structures, and also for computer algebra.
Topics of recent and current interest include:
- Performance of toric, affine variety, and algebraic geometry codes.
- Decoding algorithms.
- Applications of Gröbner basis theory.
- Multivariate polynomials over finite fields.
- Network coding.
- Algebraic function field theory.
- Secret sharing schemes.
- Secure Multiparty Computation.
- Code based cryptography.
Members of the research group and their research interest:
- Olav Geil (professor mso) works on affine variety and algebraic geometry codes. He studies their parameters, their decoding algorithms and their applications in secret sharing schemes. Olav also takes an interest in multivariate polynomials over finite fields and in algebraic function field theory. Furthermore, he works on network coding.
- Diego Ruano (associate professor) works on algebraic coding theory which includes aspects of algebraic function fields, algebraic geometry codes and decoding algorithms. Diego also studies code-based cryptography, secret sharing and network coding.
- Ignacio Cascudo (assistant professor) works on secret sharing and secure multiparty computation.
- Tom Høholdt (adjunct professor) works on algebraic coding theory, sequence design, signal analysis and other areas of applied (discrete) mathematics.
- Umberto Martínez-Peñas (PhD student) works on secret sharing, algebraic geometry codes, network coding, and subspace codes.