Zobrazeno 1 - 10
of 308
pro vyhledávání: '"Ruano, Diego"'
Autor:
Camps-Moreno, Eduardo, López, Hiram H., Matthews, Gretchen L., Ruano, Diego, San-José, Rodrigo, Soprunov, Ivan
Publikováno v:
Quantum Inf Process 23, 230 (2024)
CSS-T codes were recently introduced as quantum error-correcting codes that respect a transversal gate. A CSS-T code depends on a CSS-T pair, which is a pair of binary codes $(C_1, C_2)$ such that $C_1$ contains $C_2$, $C_2$ is even, and the shorteni
Externí odkaz:
http://arxiv.org/abs/2312.17518
Autor:
Ruano, Diego, San-José, Rodrigo
Long quantum codes using projective Reed-Muller codes are constructed. Projective Reed-Muller are evaluation codes obtained by evaluating homogeneous polynomials at the projective space. We obtain asymmetric and symmetric quantum codes by using the C
Externí odkaz:
http://arxiv.org/abs/2312.15308
Autor:
Ruano, Diego, San-José, Rodrigo
By solving a problem regarding polynomials in a quotient ring, we obtain the relative hull and the Hermitian hull of projective Reed-Muller codes over the projective plane. The dimension of the hull determines the minimum number of maximally entangle
Externí odkaz:
http://arxiv.org/abs/2312.13921
A Private Information Retrieval (PIR) protocol based on coding theory for a single server is proposed. It provides computational security against linear algebra attacks, addressing the main drawback of previous PIR proposals based on coding theory. T
Externí odkaz:
http://arxiv.org/abs/2311.04688
Matrix-product constructions giving rise to locally recoverable codes are considered, both the classical $r$ and $(r,\delta)$ localities. We study the recovery advantages offered by the constituent codes and also by the defining matrices of the matri
Externí odkaz:
http://arxiv.org/abs/2310.15703
Explicit bases for the subfield subcodes of projective Reed-Muller codes over the projective plane and their duals are obtained. In particular, we provide a formula for the dimension of these codes. For the general case over the projective space, we
Externí odkaz:
http://arxiv.org/abs/2307.09298
We study the subfield subcodes of projective Reed-Solomon codes and their duals: we provide bases for these codes and estimate their parameters. With this knowledge, we can construct symmetric and asymmetric entanglement-assisted quantum error-correc
Externí odkaz:
http://arxiv.org/abs/2304.08121
Autor:
Anderson, Sarah E., Camps-Moreno, Eduardo, López, Hiram H., Matthews, Gretchen L., Ruano, Diego, Soprunov, Ivan
Given two $q$-ary codes $C_1$ and $C_2$, the relative hull of $C_1$ with respect to $C_2$ is the intersection $C_1\cap C_2^\perp$. We prove that when $q>2$, the relative hull dimension can be repeatedly reduced by one, down to a certain bound, by rep
Externí odkaz:
http://arxiv.org/abs/2212.14521
Quantum error-correcting codes with good parameters can be constructed by evaluating polynomials at the roots of the polynomial trace. In this paper, we propose to evaluate polynomials at the roots of trace-depending polynomials (given by a constant
Externí odkaz:
http://arxiv.org/abs/2208.06187
We consider an homogeneous ideal $I$ in the polynomial ring $S=K[x_1,\dots,$ $x_m]$ over a finite field $K=\mathbb{F}_q$ and the finite set of projective rational points $\mathbb{X}$ that it defines in the projective space $\mathbb{P}^{m-1}$. We conc
Externí odkaz:
http://arxiv.org/abs/2202.04683