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DTU Compute
Department of Applied Mathematics and Computer Science
Technical University of Denmark
Matematiktorvet
Building 303 B, room 150
2800 Kgs. Lyngby
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.
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