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