Open AccessQuadratic recursive towers of function fields over $\mathbb{F}_2$
Author(s) -
Henning Stichtenoth,
Seher Tutdere
Publication year - 2015
Publication title -
turkish journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.454
H-Index - 27
eISSN - 1303-6149
pISSN - 1300-0098
DOI - 10.3906/mat-1411-42
Subject(s) - mathematics , tower , combinatorics , rational function , quadratic equation , finite field , integer (computer science) , quadratic function , function (biology) , invariant (physics) , algebraic number , degree (music) , field (mathematics) , discrete mathematics , mathematical analysis , pure mathematics , mathematical physics , geometry , physics , civil engineering , evolutionary biology , computer science , acoustics , engineering , biology , programming language
Let F = (F-n)(n >= 0) be a quadratic recursive tower of algebraic function fields over the finite field F-2 i.e. F is a recursive tower such that [F-n : Fn-l] = 2 for all n >= 1. For any integer r >= 1, let beta(r)(F) := lim(n ->infinity)B(r)(F-n)/g(F-n) where B-r(F-n) is the number of places of degree r and g(F-n) is the genus, respectively, of F-n/F-2. In this paper we give a classification of all rational functions f(X, Y) is an element of F-2 (X, Y) that may define a quadratic recursive tower F over F-2 with at least one positive invariant beta(r)(F). Moreover, we estimate beta(1)(F)for each such tower