The Gilbert-Varshamov (GV) bound is a classical existential result in coding theory. It implies that a random linear binary code of rate ε² has relative distance at least 1/2 - O(ε) with high probability. However, it is a major challenge to construct explicit codes with similar parameters. One hope to derandomize the Gilbert-Varshamov construction ...
[ES] Este trabajo consiste en la utilización de dos prototipos de vehículos autónomos no tripulados, ambos con un sistema de conducción basado en Arduino y equipados con distintos sensores, que serán capaces de comunicarse entre sí mediante módulos Bluetooth. Mediante una plataforma de pruebas a modo de circuito, dichos vehículos se moverán uno det...
Published in SN Applied Sciences
A common method of generalizing binary to multi-class classification is the error correcting code (ECC). ECCs may be optimized in a number of ways, for instance by making them orthogonal. Here we test two types of orthogonal ECCs on seven different datasets using three types of binary classifier and compare them with three other multi-class methods...
Any integral convex polytope $P$ in $\mathbb{R}^N$ provides a $N$-dimensional toric variety $X_P$ and an ample divisor $D_P$ on this variety. This paper gives an explicit construction of the algebraic geometric error-correcting code on $X_P$ , obtained by evaluating global section of $\mathcal{L}(D_P)$ on every rational point of $X_P$. This work pr...
Today, most public-key cryptosystems used to ensure the privacy and authenticity of communications rely on the hardness of number theoretic problems. For instance, the security of the RSA algorithm is based on the fact that factoring a product of large prime numbers is computationally hard. However, in 1994, Shor proposed an algorithm to efficientl...
La conception d’ordinateurs quantiques aura un impact majeur sur la cryptographie que nous utilisons tous les jours pour sécuriser nos communications, en particulier sur la cryptographie dite asymétrique. De plus, la multiplication des objets connectés dans notre quotidien et leurs limitations en terme de capacité de calcul et de mémoire disponible...
After giving a new interpretation of the skew metric defined in [4], we show that the decoding algorithm of [2] for skew Reed-Solomon codes remains valid with respect to this metric.
Published in SN Computer Science
Stream cipher encryption works by modulo-2 adding plaintext bits to keystream bits, which are in turn produced by successively updating a finite-state machine initialized to a secret starting state. PudgyTurtle is a way to encode the plaintext in a keystream-dependent manner before encryption. Since it can use keystream from any stream cipher, Pudg...
In 2004 Atserias, Kolaitis and Vardi proposed OBDD-based propositional proof systems that prove unsatisfiability of a CNF formula by deduction of identically false OBDD from OBDDs representing clauses of the initial formula. All OBDDs in such proofs have the same order of variables. We initiate the study of OBDD based proof systems that additionall...
