# 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

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topChen, 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 -

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