Institute for Mathematics and Its Applications

Talk abstract:

The Support Splitting Algorithm and Some of Its Applications

Nicolas Sendrier, INRIA-Rocquencourt

We define a signature as a property of a code and of one of its positions which is invariant when the support is permuted ; for instance the weight distribution of the code punctured in the position is a signature. The discriminancy of a signature is measured by how often it will be different for two distinct positions of the same code. We designed an algorithm, using a signature, able to split the support of a code into the orbits of its permutation group. In particular, if the permutation group is trivial, we can distinguish any two positions of a code. For this algorithm to be practical, we need a signature both discriminant an easy to compute. This is the case of the weight enumerator of the hull (intersection of code with its dual). We will present some applications of the support splitting algorithm in the binary case: the "code equivalence problem", the characterization of weak keys in McEliece's cryptosystem and the computation of permutation groups.

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