Tom Høholdt

Tom Høholdt

Professor emeritus

Department of Applied Mathematics and Computer Science

Technical University of Denmark


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 A modern digital system of communication uses advanced mathematics in a great number of ways. When information is stored or transmitted one can not be sure that the data one receives or reads is the same as the transmitted or stored. If A wants to transmit information to B this is first represented as efficient as possible and then a codeword is created by adding extra symbols. This proces is called encoding. The word treceived by B is changed by noise in the communication channel but using the extra symbols it is often, or at least with high probability, possible to recover the sent word. This proces is called decoding. When constructing codes one wants 1) the codes should have a ( mathematical) structure such that the en- and decoding algorithms have low complexity and 2) The code should be able to correct the maximal number of errors using a minimum number of redundant symbols. The mathematical problems that arises in connection with constrution and use of error-correcting codes can be attacjed using algebraic, geometric and combinatorial methods and even if the questions one wants to answer have a technical source it leads to a long series of important and intersting mathematical problems.
The coding group at DTU has for many years contributed significantly to the solution of this kind of problems.