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pro vyhledávání: '"Berardini, Elena"'
We characterise abelian surfaces defined over finite fields containing no curves of genus less than or equal to $3$. Firstly, we complete and expand the characterisation of isogeny classes of abelian surfaces with no curves of genus up to $2$ initiat
Externí odkaz:
http://arxiv.org/abs/2408.02493
Autor:
Berardini, Elena, Caruso, Xavier
We introduce the sum-rank metric analogue of Reed-Muller codes, which we called linearized Reed-Muller codes, using multivariate Ore polynomials. We study the parameters of these codes, compute their dimension and give a lower bound for their minimum
Externí odkaz:
http://arxiv.org/abs/2405.09944
Publikováno v:
Designs, Codes and Cryptography (2024)
We investigate CSS and CSS-T quantum error-correcting codes from the point of view of their existence, rarity, and performance. We give a lower bound on the number of pairs of linear codes that give rise to a CSS code with good correction capability,
Externí odkaz:
http://arxiv.org/abs/2310.16504
Autor:
Berardini, Elena, Caruso, Xavier
Publikováno v:
IEEE Transactions on Information Theory, vol. 70, no. 5, pp. 3345-3356, May 2024
We introduce the first geometric construction of codes in the sum-rank metric, which we called linearized Algebraic Geometry codes, using quotients of the ring of Ore polynomials with coefficients in the function field of an algebraic curve. We study
Externí odkaz:
http://arxiv.org/abs/2303.08903
Publikováno v:
ACM Communications in Computer Algebra, Volume 57, Issue 4 (December 2023), 200 - 229
In 1874 Brill and Noether designed a seminal geometric method for computing bases of Riemann-Roch spaces. From then, their method has led to several algorithms, some of them being implemented in computer algebra systems. The usual proofs often rely o
Externí odkaz:
http://arxiv.org/abs/2208.12725
Autor:
Berardini, Elena, Nardi, Jade
In this paper we give an upper bound on the number of rational points on an irreducible curve $C$ of degree $\delta$ defined over a finite field $\mathbb{F}_q$ lying on a Frobenius classical surface $S$ embedded in $\mathbb{P}^3$. This leads us to in
Externí odkaz:
http://arxiv.org/abs/2111.09578
We consider the finite set of isogeny classes of $g$-dimensional abelian varieties defined over the finite field $\mathbb{F}_q$ with endomorphism algebra being a field. We prove that the class within this set whose varieties have maximal number of ra
Externí odkaz:
http://arxiv.org/abs/2101.12664
We prove lower bounds for the minimum distance of algebraic geometry codes over surfaces whose canonical divisor is either nef or anti-strictly nef and over surfaces without irreducible curves of small genus. We sharpen these lower bounds for surface
Externí odkaz:
http://arxiv.org/abs/1912.07450
Akademický článek
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Publikováno v:
Finite Fields and Their Applications, Elsevier, 2021
We provide a theoretical study of Algebraic Geometry codes constructed from abelian surfaces defined over finite fields. We give a general bound on their minimum distance and we investigate how this estimation can be sharpened under the assumption th
Externí odkaz:
http://arxiv.org/abs/1904.08227