PhD Dissertation: Leyla Ateş | Manufacturing Engineering

PhD Dissertation: Leyla Ateş

PhD Dissertation: Leyla Ateş

On Lattices from Function Fields

 

 

Leyla Ates
Mathematics, PhD Dissertation, 2017

 

Thesis Jury

Prof.  Cem Guneri (Thesis Advisor),

Prof. Alev Topuzoglu,

Prof. Albert Levi,

Assist. Prof. Seher Tutdere,

Assoc. Prof. Alp Bassa

 

 

Date & Time: April 25, 2017 –  2:30 PM

Place: FENS 2008

Keywords : function field lattices, well-roundedness, kissing number

 

Abstract

 

 

In this thesis, we study the lattices L associated to a function field F over a finite field and a subset P of the set of places of F, which are the so-called functon field lattices. We mainly explore the well-roundedness property of L. In previous papers, P is always chosen to be the set of all rational places of F. We extend the definition of function field lattices to the case where P may contain places of any degree. We investigate the basic properties of L such as rank, determinant, minimum distance and kissing number. It is well-known that lattices from elliptic or Hermitian function fields are well-rounded. We show that, in contrast, well-roundedness does not hold for lattices associated to a large class of function fields, including hyperelliptic function fields.