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pro vyhledávání: '"Chara, María"'
In this work we investigate the problem of producing iso-dual algebraic geometry (AG) codes over a finite field $\mathbb{F}_q$ with $q$ elements. Given a finite separable extension $\mathcal{M}/\mathcal{F}$ of function fields and an iso-dual AG-code
Externí odkaz:
http://arxiv.org/abs/2311.08992
We construct families of locally recoverable codes with availability $t\geq 2$ using fiber products of curves, determine the exact minimum distance of many families, and prove a general theorem for minimum distance of such codes. The paper concludes
Externí odkaz:
http://arxiv.org/abs/2204.03755
In this paper we initiate the study of cyclic algebraic geometry codes. We give conditions to construct cyclic algebraic geometry codes in the context of algebraic function fields over a finite field by using their group of automorphisms. We prove th
Externí odkaz:
http://arxiv.org/abs/2106.08884
Given a suitable extension $F'/F$ of algebraic function fields over a finite field $\mathbb{F}_q$, we introduce the conorm code $\text{Con}_{F'/F}(\mathcal{C})$ defined over $F'$ which is constructed from an algebraic geometry code $\mathcal{C}$ defi
Externí odkaz:
http://arxiv.org/abs/1910.10753
We study the asymptotic behavior of a family of algebraic geometry codes, which we call block-transitive, that generalizes the classes of transitive and quasi-transitive codes. We prove, by using towers of algebraic function fields, that there are se
Externí odkaz:
http://arxiv.org/abs/1710.02395
Publikováno v:
Designs, Codes & Cryptography; Oct2024, Vol. 92 Issue 10, p2743-2767, 25p
We study the asymptotic behavior of a family of algebraic geometry codes which are 4-quasi transitive linear codes. We prove that this family is asymptotically good over many prime fields using towers of algebraic function fields.
Comment: Main
Comment: Main
Externí odkaz:
http://arxiv.org/abs/1603.03398
Autor:
Chara, Maria, Toledano, Ricardo
In this work, we give sufficient conditions in order to have finite ramification locus in sequences of function fields defined by different kind of Kummer extensions. These conditions can be easily implemented in a computer to generate several exampl
Externí odkaz:
http://arxiv.org/abs/1402.1387
Publikováno v:
In Journal of Symbolic Computation November-December 2018 89:121-128
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