18 citations · 54 across the 57 of their papers we have counts for
55 papers · 1 filter
On permutation-invariant construction of glued lattices
Maria Fernanda Zordan Bonini, Lenny Fukshansky
Given a permutation on letters, we consider lattices spanned by an orbit of one vector in under the action of by permutation of the coordi…
Structured lattices and their applications to security
Lenny Fukshansky, Camilla Hollanti, Rahinatou Y. Njah Nchiwo
Euclidean lattices are an interesting object of study in many regards and can have a rich structure arising from various constructions, e.g., from number field extensions. A partic…
On indecomposable elements in lattices
Lenny Fukshansky, Filiana Kostopoulou
We study the distribution of indecomposable elements in Euclidean lattices. A positive element in a lattice is called indecomposable if it cannot be represented as a sum of two oth…
Normal bases of small height in Galois number fields
Lenny Fukshansky, Sehun Jeong
Let be a number field of degree so that is a Galois extension. The {\it normal basis theorem} states that has a -basis consisting of algebraic…
On lattices generated by algebraic conjugates of prime degree
Lenny Fukshansky, Evelyne Knight
We consider Euclidean lattices spanned by images of algebraic conjugates of an algebraic number under Minkowski embedding, investigating their rank, properties of their automorphis…
Integral zeros of quadratic polynomials avoiding sublattices
Lenny Fukshansky, Sehun Jeong
Assuming an integral quadratic polynomial with nonsingular quadratic part has a nontrivial zero on an integer lattice outside of a union of finite-index sublattices, we prove that…