Mathematics for Communication
Since Shannon's seminal paper in 1948 the theory of communication has developed into a huge research area, including a diversity of topics such as error-correcting codes, cryptography, secret sharing, steganography, source coding, and network coding.
A wide range of mathematical disciplines are involved in the research area, this includes 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. Often the study of communication theory also results in achievements within purely theoretical areas which is, for instance, 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 and algebraic geometry codes
- Decoding algorithms
- Applications of Gröbner basis theory
- Multivariate polynomials over finite fields
- Network coding
- Algebraic function field theory.
Members of the research group and their research interests:
- Olav Geil works on affine variety and algebraic geometry codes - their parameters as well as decoding algorithms. Olav also studies multivariate polynomials over finite fields and takes an interest in algebraic function field theory. Furthermore, he works within network coding.
- Diego Ruano works on toric and algebraic geometry codes which includes studying aspects of algebraic function fields. Diego also studies matrix-product codes, their parameters and decoding algorithms. Moreover, he works within network coding.
- Stefano Martin studies secret sharing. He has also works on small-bias spaces and relative generalized Hamming weights.
Information on relevant publications can be found via the VBN Database.