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.