On lattices generated by finite Abelian groups

A Böttcher, L Fukshansky, SR Garcia… - SIAM Journal on Discrete …, 2015‏ - SIAM
This paper is devoted to the study of lattices generated by finite Abelian groups. Special
species of such lattices arise in the exploration of elliptic curves over finite fields. In the case …

Generation of" independent" points on elliptic curves by means of Mordell--Weil lattices

D Koshelev - Cryptology ePrint Archive, 2022‏ - eprint.iacr.org
This article develops a novel method of generating``independent''points on an ordinary
elliptic curve over a finite field of large characteristic. Such points are actively used, eg, in the …

Lattices from equiangular tight frames

A Böttcher, L Fukshansky, SR Garcia, H Maharaj… - Linear Algebra and its …, 2016‏ - Elsevier
We consider the set of all linear combinations with integer coefficients of the vectors of a unit
equiangular tight (k, n) frame and are interested in the question whether this set is a lattice …

On classifying Minkowskian sublattices

W Keller, J Martinet, A Schürmann - Mathematics of computation, 2012‏ - ams.org
Let $\Lambda $ be a lattice in an $ n $-dimensional Euclidean space $ E $ and let
$\Lambda'$ be a Minkowskian sublattice of $\Lambda $, that is, a sublattice having a basis …

Bases of minimal vectors in lattices, II

J Martinet - Archiv der Mathematik, 2007‏ - Springer
Bases of minimal vectors in lattices, II Page 1 Arch. Math. 89 (2007), 541–551 c© 2007
Birkhäuser Verlag Basel/Switzerland 0003/889X/060541-11, published online 2007-11-09 …

Bases of minimal vectors in tame lattices

MT Damir, G Mantilla-Soler - arxiv preprint arxiv:2006.16794, 2020‏ - arxiv.org
Motivated by the behavior of the trace pairing over tame cyclic number fields, we introduce
the notion of tame lattices. Given an arbitrary non-trivial lattice $\mathcal {L} $ we construct a …

Some Mordell-Weil lattices and applications to sphere packings

G Leterrier - 2024‏ - infoscience.epfl.ch
We provide new explicit examples of lattice sphere packings in some dimensions that are
the densest known so far, using Kummer families of elliptic curves over global function fields …

[PDF][PDF] Bases of minimal vectors in lattices, I

J Martinet - Archiv der Mathematik, 2007‏ - Citeseer
We prove that a Euclidean lattice of dimension n≤ 8 which is generated by its minimal
vectors possesses a basis of minimal vectors. Résumé. Nous montrons qu'un réseau …

The linear transformation that relates the canonical and coefficient embeddings of ideals in cyclotomic integer rings

SC Batson - International Journal of Number Theory, 2017‏ - World Scientific
The geometric embedding of an ideal in the algebraic integer ring of some number field is
called an ideal lattice. Ideal lattices and the shortest vector problem (SVP) are at the core of …

On coherence and the geometry of certain families of lattices

DB Kogan - 2022‏ - search.proquest.com
The coherence of a lattice is, roughly speaking, a measure of non-orthogonality of its
minimal vectors. It was introduced to lattices (by analogy with frame theory) by L …