We show that there is a way to define a nontrivial (partial) order onmonomials so that the monomials generating a polar code devised for a binary-input symmetric channel always form a decreasing set.Expand

We extend the notion of regular sequence ([Mac16]) to overdetermined system of algebraic equations. We study generic properties of Grobner bases and analyse precisely the behavior of the F5 [Fau02]… Expand

We study the complexity of Grobner bases computation, in particular in the generic situation where the variables are in simultaneous Noether position with respect to the system.Expand

We present complexity results for solving "typical"overdetermined algebraic systems over GF(2) with solutions in GF(2) using Grobner bases. They are useful for instance to predictthe complexity of an… Expand

We compute the asymptotic expansion of the degree of regularity for overdetermined semi-regular sequences of algebraic equations. This degree implies bounds for the generic complexity of Gröbner… Expand

We analyze a new key recovery attack against the Quasi-Cyclic MDPC McEliece scheme and give under certain hypothesis an algorithm that is able to solve a key equation relating the public key to the private key.Expand

The present proposal is a key encapsulation scheme based on a Niederreiter–like public key encryption scheme using binary quasi–cyclic Goppa codes.Expand

Polar codes discovered by Arikan form a very powerful family of codes attaining many information theoretic limits in the fields of error correction and source coding.Expand

In this paper, starting from Ourivski and Johansson's algebraic modelling of the problem into a system of polynomial equations, we show how to augment this system with easily computed equations so that the augmented system is solved much faster via Groebner bases.Expand