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Computing Groebner Bases for Finding Codewords of Small
                             Weight 
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Daniel Augot
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Date: July 19th (Friday)\\
Time:  17:00-17:30\\

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Abstract
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We describe a relationship between codewords of small weight in codes and algebraic systems of
equations. These systems are constructed from the (generalized) Newton's identities, and solving
these systems is equivalent to find codewords of weight less than a given weight. We propose to
compute a Groebner basis of the system, by using the Buchberger algorithm, or variants. These is a
complexity barrier, which make the method inefficient for long codes. However, for small length,
valuable information is obtained on codewords, because their Fourier transform is then known.
Examples are given. 

