Quadratic recursive towers of function fields over $\mathbb{F}_2$
نویسندگان
چکیده
منابع مشابه
Towers of Function Fields over Non-prime Finite Fields
Over all non-prime finite fields, we construct some recursive towers of function fields with many rational places. Thus we obtain a substantial improvement on all known lower bounds for Ihara’s quantity A(`), for ` = p with p prime and n > 3 odd. A modular interpretation of the towers is given as well.
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Let F Fl be an algebraic function field of one variable, whose constant field is the finite field of cardinality l. Weil's theorem states that the number N=N(F ) of places of degree one of F Fl satisfies the estimate N l+1+2g l , (0.1) where g= g(F ) denotes the genus of F. It is well known that for g large with respect to l, the Weil bound (0.1) is not optimal; see [5, 9]. Drinfeld and Vladut ...
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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...
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ژورنال
عنوان ژورنال: TURKISH JOURNAL OF MATHEMATICS
سال: 2015
ISSN: 1300-0098,1303-6149
DOI: 10.3906/mat-1411-42