A New Tower Over Cubic Finite Fields
نویسندگان
چکیده
We present a new explicit tower of function fields (Fn)n≥0 over the finite field with ` = q3 elements, where the limit of the ratios (number of rational places of Fn)/(genus of Fn) is bigger or equal to 2(q2 − 1)/(q + 2). This tower contains as a subtower the tower which was introduced by Bezerra– Garcia–Stichtenoth (see [3]), and in the particular case q = 2 it coincides with the tower of van der Geer–van der Vlugt (see [12]). Many features of the new tower are very similar to those of the optimal wild tower in [8] over the quadratic field Fq2 (whose modularity was shown in [6] by Elkies).
منابع مشابه
On a tower of Ihara and its limit
Towers of function fields over a fixed finite field have attracted much attention, specially for the connections with Coding Theory and Cryptography (see [TV], [NX], [Z], [GS2] and [GS3]). Ihara was the first to realize that the so-called Hasse-Weil upper bound was weak if the genus of the function field is large with respect to the cardinality of the finite field (see [Iha]). The first explici...
متن کاملAn Explicit Tower over Cubic Finite Fields and Zink’s Lower Bound
Codes over Galois Ring Gilberto Bini We shall briefly recall some basic facts on trace codes over finite fields. In particular, we will focus on generalizations of dual Melas codes. After such an overview, we will introduce the Galois ring set-up in which we try to extend some of the techniques over fields. For these purposes, we need some results on exponential sums over Galois rings. Finally,...
متن کاملEverywhere Ramified Towers of Global Function Fields
We construct a tower of function fields F0 ⊂ F1 ⊂ . . . over a finite field such that every place of every Fi ramifies in the tower and lim genus(Fi)/[Fi : F0] <∞. We also construct a tower in which every place ramifies and limNFi/[Fi : F0] > 0, where NFi is the number of degree-1 places of Fi. These towers answer questions posed by Stichtenoth at Fq7.
متن کاملClassical Wavelet Transforms over Finite Fields
This article introduces a systematic study for computational aspects of classical wavelet transforms over finite fields using tools from computational harmonic analysis and also theoretical linear algebra. We present a concrete formulation for the Frobenius norm of the classical wavelet transforms over finite fields. It is shown that each vector defined over a finite field can be represented as...
متن کاملA graph aided strategy to produce good recursive towers over finite fields
We propose a systematic method to produce potentially good recursive towers over finite fields. The graph point of view, so as some magma and sage computations are used in this process. We also establish some theoretical functional criterion ensuring the existence of many rational points on a recursive tower. Both points are illustrated on an example, from the production process, to the theoret...
متن کامل