A criterion is given which provides a lower bound on the minimum distance of $\ mathcal{C} \otimes \mathcal{D}$ for every CSS code $\mathcal D$ and this result is applied to study the behaviour of iterated tensor powers of codes.Expand

An alternative to Sidelnikov and Shestakov attack is given by building a filtration which enables to completely recover the support and the non-zero scalars defining the secret generalized Reed–Solomon code.Expand

We give polynomial time attacks on the McEliece public key cryptosystem-based either on algebraic geometry (AG) codes or on small co-dimensional subcodes of AG codes. These attacks consist in the… Expand

A key-recovery attack when \(z =1\) and \(m\) is chosen between \(1+R+O(\frac{1}{\sqrt{n}})\) where \(R\) denotes the code rate and this attack has complexity \(O(n^6) and breaks all the parameters suggested in the literature.Expand

A polynomial time attack on the McEliece public key cryptosystem based on algebraic geometry codes allows to recover a decoding algorithm for the public key even for codes from high genus curves.Expand

The parameters of any evaluation code on a smooth quadric surface are given and a BCH structure on twists of the Segre embedding of a product of any d copies of the projective line is detected.Expand

We give an upper bound on the number of rational points of an arbitrary Zariski closed subset of a projective space over a finite field. This bound depends only on the dimensions and degrees of the… Expand

A polynomial time attack of a rank metric code based encryption scheme due to Loidreau for some parameters is presented and it is shown that the attack time is proportional to the number of parameters.Expand