Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
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
Quadratic forms of codimension 2 over finite fields containing F-4 and Artin-Schreier type curves
Date
2012-03-01
Author
Özbudak, Ferruh
Saygi, Zulfukar
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
46
views
0
downloads
Cite This
Let F-q be a finite field containing F-4. Let k >= 2 be an integer. We give a full classification of quadratic forms over F-q(k) of codimension 2 provided that certain three coefficients are from F-4. As an application of this we obtain new results on the classification of maximal and minimal curves over F-q(k) . We also give some nonexistence results on certain systems of equations over F-q(k).
Subject Keywords
Maximal curve
,
Quadratic form
,
Artin-Schreier type curve
URI
https://hdl.handle.net/11511/41850
Journal
FINITE FIELDS AND THEIR APPLICATIONS
DOI
https://doi.org/10.1016/j.ffa.2011.09.008
Collections
Department of Mathematics, Article
Suggestions
OpenMETU
Core
Quadratic forms of codimension 2 over certain finite fields of even characteristic
Özbudak, Ferruh; Saygi, Zulfukar (2011-12-01)
Let F-q be a finite field of characteristic 2, not containing F-4. Let k >= 2 be an even integer. We give a full classification of quadratic forms over F-q(k) of codimension 2 provided that certain three coefficients are from F-4. We apply this to the classification of maximal and minimal curves over finite fields.
Further results on rational points of the curve y(qn) - y = gamma xqh+1 - alpha over F-qm
Cosgun, Ayhan; Özbudak, Ferruh; SAYGI, ZÜLFÜKAR (2016-06-01)
Let q be a positive power of a prime number. For arbitrary positive integers h, n, m with n dividing m and arbitrary gamma, alpha is an element of F-qm with gamma not equal 0 the number of F-qm - rational points of the curve y(qn) - y = gamma x(qh+1) - alpha is determined in many cases (Ozbudak and Saygi, in: Larcher et al. (eds.) Applied algebra and number theory, 2014) with odd q. In this paper we complete some of the remaining cases for odd q and we also present analogous results for even q.
Multidimensional cyclic codes and Artin–Schreier type hypersurfaces over finite fields
Güneri, Cem; Özbudak, Ferruh (Elsevier BV, 2008-1)
We obtain a trace representation for multidimensional cyclic codes via Delsarte's theorem. This relates the weights of the codewords to the number of affine rational points of Artin-Schreier type hypersurfaces over finite fields. Using Deligne's and Hasse-Weil-Serre inequalities we get bounds on the minimum distance. Comparison of the bounds is made and illustrated by examples. Some applications of our results are given. We obtain a bound on certain character sums over F-2 which gives better estimates than ...
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].
Quasi constricted linear representations of abelian semigroups on Banach spaces
Emelyanov, Eduard (2002-07-24)
Let (X, ∥·∥) be a Banach space. We study asymptotically bounded quasi constricted representations of an abelian semigroup IP in L(X), i.e. representations (Tt)t∈IP which satisfy the following conditions: i) limt→∞ ∥Ttx∥ < ∞ for all x ∈ X. ii) X0:= {x ∈ X:limt→∞ ∥Ttx∥ = 0} is closed and has finite codimension. We show that an asymptotically bounded representation (Tt)t∈IP is quasi constricted if and only if it has an attractor A with Hausdorff measure of noncompactness X∥·∥1 (A) < 1 with respect to some equi...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
F. Özbudak and Z. Saygi, “Quadratic forms of codimension 2 over finite fields containing F-4 and Artin-Schreier type curves,”
FINITE FIELDS AND THEIR APPLICATIONS
, pp. 396–433, 2012, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/41850.