Morgan Barbier

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In this article we see quasi-cyclic codes as block cyclic codes. We generalize some properties of cyclic codes to quasi-cyclic ones such as generator polynomials and ideals. Indeed we show a one-to-one correspondence between ℓ-quasi-cyclic codes of length ℓm and ideals of M ℓ (Fq)[X]/(X m −1). This permits to construct new classes of codes, namely quasi-BCH(More)
Different variants of the code-based McEliece cryptosystem were proposed to reduce the size of the public key. All these variants use very structured codes, which open the door to new attacks exploiting the underlying structure. In this paper, we show that the quasi-dyadic variant can be designed to resist all known attacks. In light of a new study on list(More)
—In this paper we study generalized Reed-Solomon codes (GRS codes) over commutative, noncommutative rings, show that the classical Welch-Berlekamp and Guruswami-Sudan decoding algorithms still hold in this context and we investigate their complexities. Under some hypothesis, the study of non-commutative generalized Reed-Solomon codes over finite rings leads(More)
We study the list-decoding problem of alternant codes (which includes obviously that of classical Goppa codes). The major consideration here is to take into account the (small) size of the alphabet. This amounts to comparing the generic Johnson bound to the q-ary Johnson bound. The most favourable case is q = 2, for which the decoding radius is(More)
In 1998 Crandall introduced a method based on coding theory to secretly embed a message in a digital support such as an image. Later Fridrich et al. improved this method to minimize the distortion introduced by the embedding; a process called wet paper. However, as previously emphasized in the literature, this method can fail during the embedding step. Here(More)
In this paper, we deal with the proof of ownership or legitimate usage of a digital content, such as an image, in order to tackle the illegitimate copy. The proposed scheme based on the combination of the watermarking and cancelable biometrics does not require a trusted third party, all the exchanges are between the provider and the customer. The use of(More)
Extensive studies of Boolean functions are carried in many fields. The Mobius transform is often involved for these studies. In particular, it plays a central role in coincident functions, the class of Boolean functions invariant by this transformation. This class – which has been recently introduced – has interesting properties, in particular if we want to(More)
The main decoding algorithms for Reed-Solomon codes are based on a bivariate interpolation step, which is expensive in time complexity. Lot of interpolation methods were proposed in order to decrease the complexity of this procedure, but they stay still expensive. Then Koetter, Ma and Vardy proposed in 2010 a technique, called re-encoding, which allows to(More)