arXiv 1402.63012014-02-25math.NT

On cubic Kummer towers of Garcia, Stichtenoth and Thomas type

M. Chara, R Toledano

发表信息：: Journal of Number Theory, Volume 160, March 2016, Pages 666-678
DOI：: 10.1016/j.jnt.2015.07.027

英文摘要：

In this paper we initiate the study of the class of cubic Kummer type towers considered by Garcia, Stichtenoth and Thomas in 1997 by classifying the asymptotically good ones in this class.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

A problem of Beelen, Garcia and Stichtenoth on an Artin-Schreier tower in characteristic two

We study a tower of function fields of Artin-Schreier type over a finite field with $2^s$ elements. The study of the asymptotic behavior of this tower was left as an open problem by Beelen, García and Stichtenoth in $2006$. We prove that this tower is asymptotically good for $s$ even and asymptotically bad for $s$ odd.

2016-11-22math.NT

On Automorphisms and Subtowers of an asymptotically optimal Tower of Function Fields

In this article we investigate the automorphism group of an asymptotically optimal tower of function fields introduced by Garcia and Stichtenoth. In particular we provide a detailed description of the decomposition group of some rational places. This group acts on the algebraic-geometric standard codes obtained by the Garcia-Stichtenoth tower exceeding the Gilbert-Varshamov bound. The fields fixed by the decomposition groups form an asymptotically optimal non-Galois subtower, which has been first found by Bezerra and Garcia and yields an improvement for computing codes above the Gilbert-Varsha…

2013-04-08math.NT

An equality between two towers over cubic fields

Recently Bassa, Garcia and Stichtenoth constructed a tower of function fields over GF(q^3) having many rational places relative to their genera. We show that, by removing the bottom field from this tower, we obtain the same tower we would obtain by removing certain fields from a tower constructed previously by Bezerra, Garcia and Stichtenoth.

2009-05-29math.NT

On the spectrum for the genera of maximal curves over small fields

Motivated by previous computations in Garcia, Stichtenoth and Xing (2000) paper ,we discuss the spectrum $\mathbf{M}(q^2)$ for the genera of maximal curves over finite fields of order $q^2$ with $7\leq q\leq 16$. In particular, by using a result in Kudo and Harashita(2016) paper, the set $\mathbf{M}(7^2)$ is completely determined.

2016-09-15math.AGmath.NT

On the Zeta Functions of an optimal tower of function fields over $\FF_4$

In this paper we derive a recursion for the zeta function of each function field in the second Garcia-Stichtenoth tower when $q=2$. We obtain our recursion by applying a theorem of Kani and Rosen that gives information about the decomposition of the Jacobians. This enables us to compute the zeta functions explicitly of the first six function fields.

2011-05-23math.AGmath.NT