arXiv subjects

M. Chara

Publications and source records attributed to M. Chara.

5 recordsLinked to original sources

arXiv2022

Locally recoverable codes from towers of function fields

In this work we construct sequences of locally recoverable AG codes arising from a tower of function fields and give bound for the parameters of the obtained codes. In a particular case of a tower over $\mathbb{F}_{q^2}$ for any odd $q$, defined by Garcia and Stichtenoth in [GS2007], we show that the bound is sharp for the first code in the sequence, and we include a detailed analysis for the following codes in the sequence based on the distribution of rational places that split completely in the considered function field extension.

cs.IT↗

arXiv2019

A note on subtowers and supertowers of recursive towers of function fields

In this paper we study the problem of constructing non-trivial subtowers and supertowers of recursive towers of function fields over finite fields.

math.NT↗

arXiv2016

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.

math.NT↗

arXiv2014

On cubic Kummer towers of Garcia, Stichtenoth and Thomas type

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.

math.NT↗

arXiv2014

Asymptotically bad towers of function fields

In this paper we study general conditions to prove the infiniteness of the genus of certain towers of function fields over a perfect field. We show that many known examples of towers with infinite genus are particular cases of these conditions.

math.NT↗