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 …
$\Lambda'$ be a Minkowskian sublattice of $\Lambda $, that is, a sublattice having a basis …
Whitney numbers of combinatorial geometries and higher-weight Dowling lattices
A Ravagnani - SIAM Journal on Applied Algebra and Geometry, 2022 - SIAM
We study the Whitney numbers of the first kind of combinatorial geometries, in connection
with the theory of error-correcting codes. The first part of the paper is devoted to general …
with the theory of error-correcting codes. The first part of the paper is devoted to general …
Lattice polytopes, finite abelian subgroups in $\SL (n,\C) $ and coding theory
V Batyrev, J Hofscheier - arXiv preprint arXiv:1309.5312, 2013 - arxiv.org
We consider $ d $-dimensional lattice polytopes $\Delta $ with $ h^* $-polynomial $ h^*
_\Delta= 1+ h_k^* t^ k $ for $1< k<(d+ 1)/2$ and relate them to some abelian subgroups of …
_\Delta= 1+ h_k^* t^ k $ for $1< k<(d+ 1)/2$ and relate them to some abelian subgroups of …
Lattice polytopes in coding theory
I Soprunov - Journal of Algebra Combinatorics Discrete Structures …, 2015 - dergipark.org.tr
In this paper we discuss combinatorial questions about lattice polytopes motivated by recent
results on minimum distance estimation for toric codes. We also include a new inductive …
results on minimum distance estimation for toric codes. We also include a new inductive …
Lattices and codes with long shadows
ND Elkies - arXiv preprint math/9906086, 1999 - arxiv.org
In an earlier paper (math. NT/9906019) we showed that any integral unimodular lattice L of
rank n which is not isometric with Z^ n has a characteristic vector of norm at most n-8.[A" …
rank n which is not isometric with Z^ n has a characteristic vector of norm at most n-8.[A" …
Lattices and codes with long shadows
N Elkies - Mathematical Research Letters, 1995 - dash.harvard.edu
In an earlier paper we showed that any integral unimodular lattice L of rank n which is not
isometric with Z^ n has a characteristic vector of norm at most n-8.[A" characteristic vector" of …
isometric with Z^ n has a characteristic vector of norm at most n-8.[A" characteristic vector" of …
Bases of minimal vectors in lattices, III
J Martinet, A Schürmann - International Journal of Number Theory, 2012 - World Scientific
BASES OF MINIMAL VECTORS IN LATTICES, III Page 1 International Journal of Number
Theory Vol. 8, No. 2 (2012) 551–567 c World Scientific Publishing Company DOI: 10.1142/S1793042112500303 …
Theory Vol. 8, No. 2 (2012) 551–567 c World Scientific Publishing Company DOI: 10.1142/S1793042112500303 …
Toric surface codes and Minkowski length of polygons
I Soprunov, J Soprunova - SIAM Journal on Discrete Mathematics, 2009 - SIAM
In this paper we prove new lower bounds for the minimum distance of a toric surface code
C_P defined by a convex lattice polygon P⊂R^2. The bounds involve a geometric invariant …
C_P defined by a convex lattice polygon P⊂R^2. The bounds involve a geometric invariant …
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 …
Birkhäuser Verlag Basel/Switzerland 0003/889X/060541-11, published online 2007-11-09 …
[引用][C] The 48-dimensional analogues of the Leech lattice
HV Koch - Труды Математического института имени ВА …, 1995 - mathnet.ru
An even unimodular lattice Л in R4 8 is called extremal if any vector v ф 0 has squared
length (v, v)> 6. At present two extremal even unimodular lattices in R4 8 are known (see [2 …
length (v, v)> 6. At present two extremal even unimodular lattices in R4 8 are known (see [2 …