scholarly journals Optimal self-dual Z4-codes and a unimodular lattice in dimension 41

2012 ◽  
Vol 18 (3) ◽  
pp. 529-536 ◽  
Author(s):  
Masaaki Harada
Keyword(s):  
Unimodular Lattice

The geometry of H4 polytopes

2020 ◽  
Vol 20 (3) ◽  
pp. 433-444
Author(s):  
Tomme Denney ◽  
Da’Shay Hooker ◽  
De’Janeke Johnson ◽  
Tianna Robinson ◽  
Majid Butler ◽  
...  
Keyword(s):  
Unimodular Lattice ◽  
Geometric Objects ◽  
Even Unimodular Lattice

AbstractWe describe the geometry of an arrangement of 24-cells inscribed in the 600-cell. In Section 7 we apply our results to the even unimodular lattice E8 and show how the 600-cell transforms E8/2E8, an 8-space over the field F2, into a 4-space over F4 whose points, lines and planes are labeled by the geometric objects of the 600-cell.

scholarly journals The theta functions of sublattices of the Leech lattice

1986 ◽  
Vol 101 ◽  
pp. 151-179 ◽  
Author(s):  
Takeshi Kondo ◽  
Takashi Tasaka
Keyword(s):  
Automorphism Group ◽  
Euclidean Space ◽  
Theta Functions ◽  
Orthogonal Basis ◽  
Permutation Representation ◽  
Dimensional Euclidean Space ◽  
Unimodular Lattice ◽  
Mathieu Group ◽  
Leech Lattice ◽  
Even Unimodular Lattice

Let Λ be the Leech lattice which is an even unimodular lattice with no vectors of squared length 2 in 24-dimensional Euclidean space R24. Then the Mathieu Group M24 is a subgroup of the automorphism group .0 of Λ and the action on Λ of M24 induces a natural permutation representation of M24 on an orthogonal basis For , let Λm be the sublattice of vectors invariant under m:

scholarly journals Unimodular lattice triangulations as small-world and scale-free random graphs

2015 ◽  
Vol 17 (2) ◽  
pp. 023013 ◽  
Author(s):  
B Krüger ◽  
E M Schmidt ◽  
K Mecke
Keyword(s):  
Random Graphs ◽  
Small World ◽  
Unimodular Lattice ◽  
Scale Free

scholarly journals Spectral Properties of Unimodular Lattice Triangulations

2016 ◽  
Vol 163 (3) ◽  
pp. 514-543 ◽  
Author(s):  
Benedikt Krüger ◽  
Ella M. Schmidt ◽  
Klaus Mecke
Keyword(s):  
Spectral Properties ◽  
Unimodular Lattice

scholarly journals An optimal odd unimodular lattice in dimension 72

2011 ◽  
Vol 97 (6) ◽  
pp. 529-533 ◽  
Author(s):  
Masaaki Harada ◽  
Tsuyoshi Miezaki
Keyword(s):  
Unimodular Lattice

scholarly journals Lattice points in a circle for generic unimodular shears

2017 ◽  
Vol 13 (02) ◽  
pp. 291-300 ◽  
Author(s):  
Dubi Kelmer
Keyword(s):  
Elementary Proof ◽  
Counting Function ◽  
Lattice Points ◽  
Mean Square ◽  
Unimodular Lattice ◽  
The Mean

Given a unimodular lattice [Formula: see text] consider the counting function [Formula: see text] counting the number of lattice points of norm less than [Formula: see text], and the remainder [Formula: see text]. We give an elementary proof that the mean square of the remainder over the set of all shears of a unimodular lattice is bounded by [Formula: see text].

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