Some maximal function fields and additive polynomials

Date

2007-01-01

Author

GARCİA, Arnaldo
Özbudak, Ferruh

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

298
views

0
downloads

We derive explicit equations for the maximal function fields F over F-q(2n) given by F = F-q(2n) (X, Y) with the relation A(Y) = f(X), where A(Y) and f(X) are polynomials with coefficients in the finite field F-q(2n), and where A(Y) is q- additive and deg(f) = q(n) + 1. We prove in particular that such maximal function fields F are Galois subfields of the Hermitian function field H over F-q(2n) (i.e., the extension H/F is Galois).

Subject Keywords

Algebra and Number Theory

URI

https://hdl.handle.net/11511/45904

Journal

COMMUNICATIONS IN ALGEBRA

DOI

https://doi.org/10.1080/00927870601169218

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Value sets of Lattes maps over finite fields Küçüksakallı, Ömer (Elsevier BV, 2014-10-01) We give an alternative computation of the value sets of Dickson polynomials over finite fields by using a singular cubic curve. Our method is not only simpler but also it can be generalized to the non-singular elliptic case. We determine the value sets of Lattes maps over finite fields which are rational functions induced by isogenies of elliptic curves with complex multiplication.
On maximal curves and linearized permutation polynomials over finite fields Özbudak, Ferruh (Elsevier BV, 2001-08-08) The purpose of this paper is to construct maximal curves over large finite fields using linearized permutation polynomials. We also study linearized permutation polynomials under finite field extensions.
On the deformation chirality of real cubic fourfolds Finashin, Sergey (Wiley, 2009-09-01) According to our previous results, the conjugacy class of the involution induced by the complex conjugation in the homology of a real non-singular cubic fourfold determines the fourfold tip to projective equivalence and deformation. Here, we show how to eliminate the projective equivalence and obtain a pure deformation classification, that is, how to respond to the chirality problem: which cubics are not deformation equivalent to their image under a mirror reflection. We provide an arithmetical criterion of...
On algebraic K-theory of real algebraic varieties with circle action Ozan, Yıldıray (Elsevier BV, 2002-05-24) Assume that X is a compact connected orientable nonsingular real algebraic variety with an algebraic free S-1-action so that the quotient Y=X/S-1 is also a real algebraic variety. If pi:X --> Y is the quotient map then the induced map between reduced algebraic K-groups, tensored with Q, pi* : (K) over bar (0)(R(Y, C)) circle times Q --> (K) over bar (0)(R(X, C)) circle times Q is onto, where R(X, C) = R(X) circle times C, R(X) denoting the ring of entire rational (regular) functions on the real algebraic va...
The classical involution theorem for groups of finite Morley rank Berkman, A (Elsevier BV, 2001-09-15) This paper gives a partial answer to the Cherlin-Zil'ber Conjecture, which states that every infinite simple group of finite Morley rank is isomorphic to an algebraic group over an algebraically closed field. The classification of the generic case of tame groups of odd type follows from the main result of this work, which is an analogue of Aschbacher's Classical Involution Theorem for finite simple groups. (C) 2001 Academic Press.

Citation Formats

A. GARCİA and F. Özbudak, “Some maximal function fields and additive polynomials,” COMMUNICATIONS IN ALGEBRA, pp. 1553–1566, 2007, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/45904.