Classification of function fields with class number three

BİLHAN, Mehpare
Buyruk, Dilek
Özbudak, Ferruh
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 ...
Bilhan, Mehpare; Buyruk, Dilek; Özbudak, Ferruh (2019-01-01)
We list all subfields of cyclotomic function fields over rational function fields with class number three. We also determine all the imaginary abelian extensions with relative class number three, explicitly.
Efficient multiplications in F(5)5n and F(7)7n
Cenk, Murat; Özbudak, Ferruh (2011-08-15)
Efficient multiplications in finite fields of characteristics 5 and 7 are used for computing the Eta pairing over divisor class groups of the hyperelliptic curves Lee et al. (2008) [1]. In this paper, using the recent methods for multiplication in finite fields, the explicit formulas for multiplication in F(5)5n and F(7)7n are obtained with 10 multiplications in F(5)n for F(5)5n and 15 multiplications in F(7)n for F(7)7n improving the results in Cenk and Ozbudak (2008) [4], Cenk et al. (2009) [5], Lee et al...
On Fibre Products of Kummer Curves with Many Rational Points over Finite Fields
Özbudak, Ferruh; YAYLA, OĞUZ (2014-09-18)
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. (2014). Accessed 30 Sep 2014). Using the methods given in Ozbudak and Gulmez Temur (Des ...
Characterisation and enumeration of a class of semi bent quadratic Boolean functions
KOÇAK, Neşe; Koçak, Onur Ozan; Özbudak, Ferruh; SAYGI, ZÜLFÜKAR (2015-01-01)
In this paper, we consider semi-bentness of quadratic Boolean functions defined for even n and give the characterisation of these functions. Up to our knowledge, semi-bentness of this class has not been investigated before and we proved that semi-bent functions of this form exist only for 6|n. Furthermore, we present a method for enumeration of semi-bent and bent functions in certain classes. Using this method we find the exact number of semi-bent functions of this form. Moreover, we complete some previous ...
Citation Formats
M. BİLHAN, D. Buyruk, and F. Özbudak, “Classification of function fields with class number three,” JOURNAL OF PURE AND APPLIED ALGEBRA, pp. 5097–5116, 2015, Accessed: 00, 2020. [Online]. Available: