Zobrazeno 1 - 10
of 206
pro vyhledávání: '"Zémor, Gilles"'
Autor:
Couvreur, Alain, Zémor, Gilles
Freiman's $3k-4$ Theorem states that if a subset $A$ of $k$ integers has a Minkowski sum $A+A$ of size at most $3k-4$, then it must be contained in a short arithmetic progression. We prove a function field analogue that is also a generalisation: it s
Externí odkaz:
http://arxiv.org/abs/2408.00183
Autor:
Rozendaal, Wouter, Zémor, Gilles
Kitaev's toric code is arguably the most studied quantum code and is expected to be implemented in future generations of quantum computers. The renormalisation decoders introduced by Duclos-Cianci and Poulin exhibit one of the best trade-offs between
Externí odkaz:
http://arxiv.org/abs/2309.12165
Autor:
Leverrier, Anthony, Zémor, Gilles
We introduce sequential and parallel decoders for quantum Tanner codes. When the Tanner code construction is applied to a sufficiently expanding square complex with robust local codes, we obtain a family of asymptotically good quantum low-density par
Externí odkaz:
http://arxiv.org/abs/2208.05537
We introduce a new rank-based key encapsulation mechanism (KEM) with public key and ciphertext sizes around 3.5 Kbytes each, for 128 bits of security, without using ideal structures. Such structures allow to compress objects, but give reductions to s
Externí odkaz:
http://arxiv.org/abs/2206.11961
Autor:
Leverrier, Anthony, Zémor, Gilles
Publikováno v:
Proceedings of SODA 2023
We introduce and analyse an efficient decoder for the quantum Tanner codes of that can correct adversarial errors of linear weight. Previous decoders for quantum low-density parity-check codes could only handle adversarial errors of weight $O(\sqrt{n
Externí odkaz:
http://arxiv.org/abs/2206.07571
Autor:
Leverrier, Anthony, Zémor, Gilles
Tanner codes are long error correcting codes obtained from short codes and a graph, with bits on the edges and parity-check constraints from the short codes enforced at the vertices of the graph. Combining good short codes together with a spectral ex
Externí odkaz:
http://arxiv.org/abs/2202.13641
Autor:
Barg, Alexander, Zémor, Gilles
Publikováno v:
IEEE Transactions on Information Theory, 2022, vol. 68, no. 12, pp. 7787-7797
Consider an assignment of bits to the vertices of a connected graph $G(V,E)$ with the property that the value of each vertex is a function of the values of its neighbors. A collection of such assignments is called a {\em storage code} of length $|V|$
Externí odkaz:
http://arxiv.org/abs/2110.02378
Autor:
Oggier, Frédérique, Zémor, Gilles
We consider oblivious transfer protocols performed over binary symmetric channels in a malicious setting where parties will actively cheat if they can. We provide constructions purely based on coding theory that achieve an explicit positive rate, the
Externí odkaz:
http://arxiv.org/abs/2008.13551
The HQC encryption framework is a general code-based encryption scheme for which decryption returns a noisy version of the plaintext. Any instantiation of the scheme will therefore use an error-correcting procedure relying on a fixed auxiliary code.
Externí odkaz:
http://arxiv.org/abs/2005.10741
Decodable quantum LDPC codes beyond the $\sqrt{n}$ distance barrier using high dimensional expanders
Constructing quantum LDPC codes with a minimum distance that grows faster than a square root of the length has been a major challenge of the field. With this challenge in mind, we investigate constructions that come from high-dimensional expanders, i
Externí odkaz:
http://arxiv.org/abs/2004.07935