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pro vyhledávání: '"Beelen, Peter"'
Let $\mathcal{H}_q$ denote the Hermitian curve in $\mathbb{P}^2$ over $\mathbb{F}_{q^2}$ and $\mathcal{C}_d$ be an irreducible plane projective curve in $\mathbb{P}^2$ also defined over $\mathbb{F}_{q^2}$ of degree $d$. Can $\mathcal{H}_q$ and $\math
Externí odkaz:
http://arxiv.org/abs/2407.13521
In this article we continue the work started in arXiv:2303.00376v1, explicitly determining the Weierstrass semigroup at any place and the full automorphism group of a known $\mathbb{F}_{q^2}$-maximal function field $Y_3$ having the third largest genu
Externí odkaz:
http://arxiv.org/abs/2404.18808
The problem of understanding whether two given function fields are isomorphic is well-known to be difficult, particularly when the aim is to prove that an isomorphism does not exist. In this paper we investigate a family of maximal function fields th
Externí odkaz:
http://arxiv.org/abs/2404.14179
Autor:
Beelen, Peter, Montanucci, Maria
In this paper we consider algebraic geometry (AG) codes: a class of codes constructed from algebraic codes (equivalently, using function fields) by Goppa. These codes can be list-decoded using the famous Guruswami-Sudan (GS) list-decoder, but the gen
Externí odkaz:
http://arxiv.org/abs/2307.04203
Autor:
Beelen, Peter, Neiger, Vincent
In this article, we present a fast algorithm performing an instance of the Guruswami-Sudan list decoder for algebraic geometry codes. We show that any such code can be decoded in $\tilde{O}(s^2\ell^{\omega-1}\mu^{\omega-1}(n+g) + \ell^\omega \mu^\ome
Externí odkaz:
http://arxiv.org/abs/2304.07083
In this article we explicitly determine the Weierstrass semigroup at any point and the full automorphism group of a known $\mathbb{F}_{q^2}$-maximal curve $\mathcal{X}_3$ having the third largest genus. This curve arises as a Galois subcover of the H
Externí odkaz:
http://arxiv.org/abs/2303.00376
Autor:
Beelen, Peter
Since Serre gave his famous Harvard lectures in 1985 on various aspects of the theory of algebraic curves defined over a finite field, there have been many developments. In this survey article, an overview will be given on the developments concerning
Externí odkaz:
http://arxiv.org/abs/2203.03310
We present an efficient list decoding algorithm in the style of Guruswami-Sudan for algebraic geometry codes. Our decoder can decode any such code using $\tilde{\mathcal O}(s\ell^{\omega}\mu^{\omega-1}(n+g))$ operations in the underlying finite field
Externí odkaz:
http://arxiv.org/abs/2203.00940
Let $\mathcal{X}$ be a projective, irreducible, nonsingular algebraic curve over the finite field $\mathbb{F}_q$ with $q$ elements and let $|\mathcal{X}(\mathbb{F}_q)|$ and $g(\mathcal X)$ be its number of rational points and genus respectively. The
Externí odkaz:
http://arxiv.org/abs/2201.00602
In this article, we present a new construction of evaluation codes in the Hamming metric, which we call twisted Reed-Solomon codes. Whereas Reed-Solomon (RS) codes are MDS codes, this need not be the case for twisted RS codes. Nonetheless, we show th
Externí odkaz:
http://arxiv.org/abs/2107.06945