Groebner Basis: A Bridge between Coding Theory and Computer Algebra
Date: July 17th (Wednesday)
Time: 16:20-17:00
Abstract
In this talk we give a survey of
- when the concept of Groebner basis has been introduced into the world
of coding theory;
- how the concept of Groebner basis has been applied to construction and
decoding of error-correcting codes,
and discuss some important roles of Groebner basis in recent development of
coding theory. It is emphasized that Buchberger's algorithm and its
relatives take their parts just at the point of contact of coding theory
with system theory and that Groebner basis is a key not only to full
decoding of the most frequently used error-correcting codes such as
Reed-Solomon and Bose-Chaudhuri-Hocquenghem codes but also to construction
and efficient decoding method of the next generation of error-correcting
codes called algebraic-geometry codes.
