Alp Bassa

Towards a characterization of subfields of the Deligne-Lusztig function fields

In this paper, we give a characterization of subgroups contained in the decomposition group A(P∞) of a rational place P∞ by means of a necessary and sufficient condition for each of the three types of function fields of Deligne–Lusztig curves. In particular, we translate the problems on the genera of subfields of the Deligne–Lusztig function fields to the combinatorial problems concerning some specific vector spaces and their dimensions. This allows us to determine the genera set consisting of all the genera of the fixed fields of subgroups of the decomposition group A(P∞) for the Hermitian function field over Fq where q is a power of an odd prime. Promising results pertaining to the genera of subfields of the other types of Deligne–Lusztig function fields are provided as well. Indeed, it turns out that we improve many previous results given by Garcia–Stichtenoth–Xing, Giulietti–Korchmaros–Torres and Cakcak–Ozbudak on the subfields of function fields of Deligne–Lusztig curves.

A complete characterization of Galois subfields of the generalized Giulietti–Korchmáros function field

Abstract We give a complete characterization of all Galois subfields of the generalized Giulietti–Korchmaros function fields C n / F q 2 n for n ≥ 5 . Calculating the genera of the corresponding fixed fields, we find new additions to the list of known genera of maximal function fields.

3D object recognition using invariants of 2D projection curves

This paper presents a new method for recognizing 3D objects based on the comparison of invariants of their 2D projection curves. We show that Euclidean equivalent 3D surfaces imply affine equivalent 2D projection curves that are obtained from the projection of cross-section curves of the surfaces onto the coordinate planes. Planes used to extract cross-section curves are chosen to be orthogonal to the principal axes of the defining surfaces. Projection curves are represented using implicit polynomial equations. Affine algebraic and geometric invariants of projection curves are constructed and compared under a variety of distance measures. Results are verified by several experiments with objects from different classes and within the same class.

A modular interpretation of various cubic towers

Abstract In this article we give a Drinfeld modular interpretation for various towers of function fields meeting Zinks bound.

An Improvement of the Gilbert–Varshamov Bound Over Nonprime Fields

The Gilbert-Varshamov bound guarantees the existence of families of codes over the finite field F_ℓ with good asymptotic parameters. We show that this bound can be improved for all nonprime fields F_ℓ with ℓ ≥ 49 , except possibly ℓ = 125. We observe that the same improvement even holds within the class of transitive codes and within the class of self-orthogonal codes.

Self-dual codes better than the Gilbert–Varshamov bound

We show that every self-orthogonal code over

Towers of function fields over non-prime finite fields

{\mathbb {F}}_q

The Hasse-Witt invariant in some towers of function fields over finite fields

Fq of length n can be extended to a self-dual code, if there exists self-dual codes of length n. Using a family of Galois towers of algebraic function fields we show that over any nonprime field