Diego Ruano
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View article: Duals of multiplicity codes
Duals of multiplicity codes Open
Multivariate multiplicity codes have been recently explored because of their importance for list decoding and local decoding. Given a multivariate multiplicity code, in this paper, we compute its dimension using Gröbner basis tools, its du…
View article: The Schur product of evaluation codes and its application to CSS-T quantum codes and private information retrieval
The Schur product of evaluation codes and its application to CSS-T quantum codes and private information retrieval Open
In this work, we study the componentwise (Schur) product of monomial-Cartesian codes by exploiting its correspondence with the Minkowski sum of their defining exponent sets. We show that $ J$-affine variety codes are well suited for such p…
View article: Binary Triorthogonal and CSS-T Codes for Quantum Error Correction
Binary Triorthogonal and CSS-T Codes for Quantum Error Correction Open
In this paper, we study binary triorthogonal codes and their relation to CSS-T quantum codes. We characterize the binary triorthogonal codes that are minimal or maximal with respect to the CSS-T poset, and we also study how to derive new t…
View article: An algebraic characterization of binary CSS-T codes and cyclic CSS-T codes for quantum fault tolerance
An algebraic characterization of binary CSS-T codes and cyclic CSS-T codes for quantum fault tolerance Open
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 t…
View article: Subfield subcodes of projective Reed-Muller codes
Subfield subcodes of projective Reed-Muller codes Open
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…
View article: Quantum error-correcting codes from projective Reed-Muller codes and their hull variation problem
Quantum error-correcting codes from projective Reed-Muller codes and their hull variation problem Open
Long quantum codes using projective Reed-Muller codes are constructed. Projective Reed-Muller codes are evaluation codes obtained by evaluating homogeneous polynomials at the projective space. We obtain asymmetric and symmetric quantum cod…
View article: Hulls of projective Reed-Muller codes over the projective plane
Hulls of projective Reed-Muller codes over the projective plane Open
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 maximal…
View article: Entanglement-assisted quantum error-correcting codes from subfield subcodes of projective Reed–Solomon codes
Entanglement-assisted quantum error-correcting codes from subfield subcodes of projective Reed–Solomon codes Open
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 e…
View article: Single Server Private Information Retrieval Protocols With Codes Over Rings
Single Server Private Information Retrieval Protocols With Codes Over Rings Open
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 codin…
View article: Optimal quantum locally recoverable codes from matrix-product construction
Optimal quantum locally recoverable codes from matrix-product construction Open
Locally recoverable codes (LRCs) are classical error-correcting codes widely used in large scale distributed and cloud storage systems. Quantum locally recoverable codes (quantum LRCs) are the quantum counterpart of classical LRCs. They al…
View article: Subfield subcodes of projective Reed-Muller codes
Subfield subcodes of projective Reed-Muller codes Open
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…
View article: Entanglement-assisted quantum error-correcting codes from subfield subcodes of projective Reed-Solomon codes
Entanglement-assisted quantum error-correcting codes from subfield subcodes of projective Reed-Solomon codes Open
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 e…
View article: Relative hulls and quantum codes
Relative hulls and quantum codes Open
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 bo…
View article: Stabilizer quantum codes defined by trace-depending polynomials
Stabilizer quantum codes defined by trace-depending polynomials Open
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 …
View article: Saturation and vanishing ideals
Saturation and vanishing ideals Open
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…
View article: An algorithmic approach to entanglement-assisted quantum error-correcting codes from the Hermitian curve
An algorithmic approach to entanglement-assisted quantum error-correcting codes from the Hermitian curve Open
We study entanglement-assisted quantum error-correcting codes (EAQECCs) arising from classical one-point algebraic geometry codes from the Hermitian curve with respect to the Hermitian inner product. Their only unknown parameter is $c$, th…
View article: Private Information Retrieval Schemes Using Cyclic Codes
Private Information Retrieval Schemes Using Cyclic Codes Open
A Private Information Retrieval (PIR) scheme allows users to retrieve data from a database without disclosing to the server information about the identity of the data retrieved. A coded storage in a distributed storage system with colludin…
View article: Private Information Schemes Using Cyclic Codes
Private Information Schemes Using Cyclic Codes Open
A Private Information Retrieval (PIR) scheme allows users to retrieve data from a database without disclosing to the server information about the identity of the data retrieved. A coded storage in a distributed storage system with colludin…
View article: Entanglement-assisted quantum error-correcting codes from RS codes and BCH codes with extension degree 2
Entanglement-assisted quantum error-correcting codes from RS codes and BCH codes with extension degree 2 Open
Entanglement-assisted quantum error correcting codes (EAQECCs) constructed from Reed-Solomon codes and BCH codes are considered in this work. It is provided a complete and explicit formula for the parameters of EAQECCs coming from any Reed…
View article: Correction to “Fulcrum: Flexible Network Coding for Heterogeneous Devices”
Correction to “Fulcrum: Flexible Network Coding for Heterogeneous Devices” Open
In the above article [1], in Section II-B.1)a, titled “Outer Encoding,” the first sentence of the second paragraph should be corrected to consistently use to denote the coded packets, i.e., this sentence should state: “For systematic oute…
View article: Asymmetric Entanglement-Assisted Quantum Error-Correcting Codes and BCH Codes
Asymmetric Entanglement-Assisted Quantum Error-Correcting Codes and BCH Codes Open
The concept of asymmetric entanglement-assisted quantum error-correcting code (asymmetric EAQECC) is introduced in this article. Codes of this type take advantage of the asymmetry in quantum errors since phase-shift errors are more probabl…
View article: High dimensional affine codes whose square has a designed minimum\n distance
High dimensional affine codes whose square has a designed minimum\n distance Open
Given a linear code $\\mathcal{C}$, its square code $\\mathcal{C}^{(2)}$ is the\nspan of all component-wise products of two elements of $\\mathcal{C}$. Motivated\nby applications in multi-party computation, our purpose with this work is to…
View article: Improved Bounds on the Threshold Gap in Ramp Secret Sharing
Improved Bounds on the Threshold Gap in Ramp Secret Sharing Open
In this paper, we consider linear secret sharing schemes over a finite field F q , where the secret is a vector in Fℓ q and each of the n shares is a single element of F q . We obtain lower bounds on the so-called threshold gap g of such s…
View article: New Binary and Ternary LCD Codes
New Binary and Ternary LCD Codes Open
LCD codes are linear codes with important cryptographic applications. Recently, a method has been presented
\nto transform any linear code into an LCD code with the same parameters when it is supported on a finite field with
\ncardinality …