On lattices from function fields

Ateş, Leyla (2017) On lattices from function fields. [Thesis]

[thumbnail of LeylaAtes_10145972.pdf] PDF

Download (553kB)


In this thesis, we study the lattices ∧p associated to a function eld F/Fq and a subset P⊆P (F), which are the so-called function eld lattices. We mainly explore the well-roundedness property of ∧p. 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 ∧p such as rank, determinant, minimum distance and kissing number. It is well-known that lattices from elliptic or Hermitian function fields are wellrounded. We show that, in contrast, well-roundedness does not hold for lattices associated to a large class of function fields, including hyperelliptic function fields.
Item Type: Thesis
Uncontrolled Keywords: Function field lattices. -- Well-roundedness. -- Kissing number. -- Fonksiyon cismi latisleri. -- Lineer bağımsız ve minimal vektörler. -- Minimal vektör sayısı.
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics
Faculty of Engineering and Natural Sciences
Depositing User: IC-Cataloging
Date Deposited: 10 Apr 2018 15:58
Last Modified: 26 Apr 2022 10:15
URI: https://research.sabanciuniv.edu/id/eprint/34408

Actions (login required)

View Item
View Item