On a generalization of Craig lattices

Hao Chen[1]

  • [1] Software Engineering Institute East China Normal University Zhong Shan North Road 3663 Shanghai 200062, P.R. China

Journal de Théorie des Nombres de Bordeaux (2013)

  • Volume: 25, Issue: 1, page 59-70
  • ISSN: 1246-7405

Abstract

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In this paper we introduce generalized Craig lattices, which allows us to construct lattices in Euclidean spaces of many dimensions in the range 3332 - 4096 which are denser than the densest known Mordell-Weil lattices. Moreover we prove that if there were some nice linear binary codes we could construct lattices even denser in the range 128 - 3272 . We also construct some dense lattices of dimensions in the range 4098 - 8232 . Finally we also obtain some new lattices of moderate dimensions such as 68 , 84 , 85 , 86 , which are denser than the previously known densest lattices.

How to cite

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Chen, Hao. "On a generalization of Craig lattices." Journal de Théorie des Nombres de Bordeaux 25.1 (2013): 59-70. <http://eudml.org/doc/275737>.

@article{Chen2013,
abstract = {In this paper we introduce generalized Craig lattices, which allows us to construct lattices in Euclidean spaces of many dimensions in the range $3332-4096$ which are denser than the densest known Mordell-Weil lattices. Moreover we prove that if there were some nice linear binary codes we could construct lattices even denser in the range $128-3272$. We also construct some dense lattices of dimensions in the range $4098-8232$. Finally we also obtain some new lattices of moderate dimensions such as $68, 84, 85, 86$, which are denser than the previously known densest lattices.},
affiliation = {Software Engineering Institute East China Normal University Zhong Shan North Road 3663 Shanghai 200062, P.R. China},
author = {Chen, Hao},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {generalized Craig lattices},
language = {eng},
month = {4},
number = {1},
pages = {59-70},
publisher = {Société Arithmétique de Bordeaux},
title = {On a generalization of Craig lattices},
url = {http://eudml.org/doc/275737},
volume = {25},
year = {2013},
}

TY - JOUR
AU - Chen, Hao
TI - On a generalization of Craig lattices
JO - Journal de Théorie des Nombres de Bordeaux
DA - 2013/4//
PB - Société Arithmétique de Bordeaux
VL - 25
IS - 1
SP - 59
EP - 70
AB - In this paper we introduce generalized Craig lattices, which allows us to construct lattices in Euclidean spaces of many dimensions in the range $3332-4096$ which are denser than the densest known Mordell-Weil lattices. Moreover we prove that if there were some nice linear binary codes we could construct lattices even denser in the range $128-3272$. We also construct some dense lattices of dimensions in the range $4098-8232$. Finally we also obtain some new lattices of moderate dimensions such as $68, 84, 85, 86$, which are denser than the previously known densest lattices.
LA - eng
KW - generalized Craig lattices
UR - http://eudml.org/doc/275737
ER -

References

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