On a generalization of Craig lattices
Journal de Théorie des Nombres de Bordeaux, Volume 25 (2013) no. 1, pp. 59-70.

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.

Dans cet article nous introduisons une généralisation des réseaux de Craig, qui nous permet de construire dans de nombreuses dimensions entre 3332 et 4096 des réseaux euclidiens plus denses que les réseaux de Mordell-Weil les plus denses connus. De plus, nous montrons que,sous réserve de l’existence de certains codes linéaires binaires, nous pouvons encore améliorer ces constructions dans l’intervalle 128-3272. Nous construisons aussi quelques réseaux denses dans les dimensions 4098-8232. Finalement nous obtenons également de nouveaux réseaux dans des dimension modérées, comme 68,84,85,86, qui sons plus denses que les réseaux connus jusqu’à présent.

Received:
Revised:
Published online:
DOI: 10.5802/jtnb.825
Classification: 52C17,  52C07,  11H31,  11H71
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Hao Chen. On a generalization of Craig lattices. Journal de Théorie des Nombres de Bordeaux, Volume 25 (2013) no. 1, pp. 59-70. doi : 10.5802/jtnb.825. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.825/

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