**On Lattices from Function Fields**

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**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

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**Abstract**

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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.