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Lattices from Hermitian function fields. (English) Zbl 1334.11049

This paper is dealing with the Rosenbloom-Tsfasman function field lattices, the lattices coming from elliptic curves and finite abelian groups. In the special case of Hermitian function fields, the authors show that the resulting lattices are generated by their minimal vectors. An estimate on the total number of minimal vectors is provided in this paper. Further, the authors study some properties of the automorphism groups of these lattices. The proofs of the main results are based on the factorization of functions with particular divisor support into lines and their inverses, which was established by G. Hiss [Indag. Math., New Ser. 15, No. 2, 223–243 (2004; Zbl 1139.05308)].

MSC:

11H06 Lattices and convex bodies (number-theoretic aspects)
11G20 Curves over finite and local fields

Citations:

Zbl 1139.05308

Software:

Magma
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References:

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