Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Open Access Guideline
Open Access Guideline
Postgraduate Thesis Guideline
Postgraduate Thesis Guideline
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
On Fibre Products of Kummer Curves with Many Rational Points over Finite Fields
Date
2014-09-18
Author
Özbudak, Ferruh
YAYLA, OĞUZ
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
221
views
0
downloads
Cite This
We determined the number of rational points of fibre products of two Kummer covers over a rational point of the projective line in a recent work of F. Ozbudak and B. G. Temur (Des Codes Cryptogr 70(3): 385-404, 2014), where we also constructed explicit examples, including a record and two new entries for the current Table of Curves with Many Points (manYPoints: Table of curves with many points. http://www.manypoints.org (2014). Accessed 30 Sep 2014). Using the methods given in Ozbudak and Gulmez Temur (Des Codes Cryptogr 70(3): 385-404, 2014), we made an exhaustive computer search over F-5 and F-7 by the contributions of O. Yayla and at the end of this search we obtained 12 records and 6 new entries for the current table; in particular, we observed that the fibre product with genus 7 and 36 rational points coincides with the Ihara bound, thus we concluded that the maximum number N-7(7) of F-7-rational points among all curves of genus 7 is 36 (Ozbudak et al., Turkish J Math 37(6): 908-913, 2013). Recently, we made another exhaustive computer search over F-11. In this paper we are representing the results as three records and three new entries for the current table.
Subject Keywords
Curves with many points
,
Algebraic function fields
URI
https://hdl.handle.net/11511/47954
DOI
https://doi.org/10.1007/978-3-319-17296-5_33
Collections
Department of Mathematics, Conference / Seminar
Suggestions
OpenMETU
Core
Explicit maximal and minimal curves over finite fields of odd characteristics
Özbudak, Ferruh (2016-11-01)
In this work we present explicit classes of maximal and minimal Artin-Schreier type curves over finite fields having odd characteristics. Our results include the proof of Conjecture 5.9 given in [1] as a very special subcase. We use some techniques developed in [2], which were not used in [1].
Classification of function fields with class number three
BİLHAN, Mehpare; Buyruk, Dilek; Özbudak, Ferruh (2015-11-01)
We give the full list of all algebraic function fields over a finite field with class number three up to isomorphism. Our list consists of explicit equations of algebraic function fields which are mutually non-isomorphic over the full constant field.
On multiplication in finite fields
Cenk, Murat; Özbudak, Ferruh (2010-04-01)
We present a method for multiplication in finite fields which gives multiplication algorithms with improved or best known bilinear complexities for certain finite fields. Our method generalizes some earlier methods and combines them with the recently introduced complexity notion (M) over cap (q)(l), which denotes the minimum number of multiplications needed in F-q in order to obtain the coefficients of the product of two arbitrary l-term polynomials modulo x(l) in F-q[x]. We study our method for the finite ...
Finite number of fibre products of Kummer covers and curves with many points over finite fields
Özbudak, Ferruh (2014-03-01)
We study fibre products of a finite number of Kummer covers of the projective line over finite fields. We determine the number of rational points of the fibre product over a rational point of the projective line, which improves the results of Ozbudak and Temur (Appl Algebra Eng Commun Comput 18:433-443, 2007) substantially. We also construct explicit examples of fibre products of Kummer covers with many rational points, including a record and two new entries for the current table (http://www.manypoints.org,...
Generalized bent functions with perfect nonlinear functions on arbitrary groups
Yılmaz, Emrah Sercan; Özbudak, Ferruh; Department of Cryptography (2012)
This thesis depends on the paper ‘Non-Boolean Almost Perfect Nonlinear Functions on Non- Abelian Groups’ by Laurent Poinsot and Alexander Pott and we have no new costructions here. We give an introduction about character theory and the paper of Poinsot and Pott, and we also compare previous definitions of bent functions with the definition of the bent function in the paper. As a conclusion, we give new theoretical definitions of bent, PN, APN ana maximum nonlinearity. Moreover, we show that bent and PN func...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
F. Özbudak and O. YAYLA, “On Fibre Products of Kummer Curves with Many Rational Points over Finite Fields,” 2014, vol. 3, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/47954.