Welcome to the home page for the Coding Theory
Group at the Department of Mathematics
of University of Turku.
The group is part of the Turku Centre for Computer Science (TUCS).
Assume that information is sent from a source over a noisy channel to a receiver. A fundamental problem of coding theory is to determine what message was sent on
the basis of the approximation that was received. The mathematical theory of error-correcting codes dates back to Shannon who in 1948 published a very remarkable
paper on the existence of good error-correcting systems. At the same time Hamming constructed perfect single-error-correcting codes.
The research carried out at the department essentially started in 1971 when
Tietäväinen solved the so-called perfect code
problem. During last decades the theory of
error-correcting codes has developed drastically. From the mathematical point of view it is an application of number theory, algebra and combinatorics. We have studied
all these areas. The mathematical coding theory is in part pure basic research, but since the applications are never very far away, many aspects have great significance
also on the practical level.
Some number theoretic problems that have been investigated or will be attacked have been considered in the chapter "Codes and Number Theory" (by Honkala and
Tietäväinen) of Handbook of Coding Theory. The monograph "Covering Codes" (by Cohen, Honkala, Litsyn and Lobstein) discusses
how we can apply algebraic and
combinatorial methods to covering radius problems.
All in all eleven PhD theses have been written about coding theory at
the Department of Mathematics at the University of Turku. The most recent
one was written in 2002 by Kalle Ranto.
The main fields of research are
At the moment the Coding Theory Group consists of eight researchers. The
leader of the group is Iiro Honkala.
For the members of the group and their publications, see
The research groups of Finnish mathematics were evaluated during the
spring 2000.
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