A lattice is called dual strongly perfect if both, the lattice and its dual, are strongly perfect. We show that there are no dual strongly perfect lattices of dimension 13 and 15.
Un réseau est dual fortement parfait si le réseau et son dual sont fortement parfaits. On démontre qu’il n’y a pas de réseau dual fortement parfait en dimension 13 et 15.
Keywords: extreme lattices, spherical designs, strongly perfect lattices, dual strongly perfect lattices
@article{JTNB_2013__25_1_147_0,
author = {Gabriele Nebe and Elisabeth Nossek and Boris Venkov},
title = {Low dimensional strongly perfect lattices. {II:} {Dual} strongly perfect lattices of dimension 13 and 15.},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {147--161},
publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
volume = {25},
number = {1},
year = {2013},
doi = {10.5802/jtnb.830},
mrnumber = {3063835},
zbl = {1271.11069},
language = {en},
url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.830/}
}
TY - JOUR AU - Gabriele Nebe AU - Elisabeth Nossek AU - Boris Venkov TI - Low dimensional strongly perfect lattices. II: Dual strongly perfect lattices of dimension 13 and 15. JO - Journal de théorie des nombres de Bordeaux PY - 2013 SP - 147 EP - 161 VL - 25 IS - 1 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.830/ DO - 10.5802/jtnb.830 LA - en ID - JTNB_2013__25_1_147_0 ER -
%0 Journal Article %A Gabriele Nebe %A Elisabeth Nossek %A Boris Venkov %T Low dimensional strongly perfect lattices. II: Dual strongly perfect lattices of dimension 13 and 15. %J Journal de théorie des nombres de Bordeaux %D 2013 %P 147-161 %V 25 %N 1 %I Société Arithmétique de Bordeaux %U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.830/ %R 10.5802/jtnb.830 %G en %F JTNB_2013__25_1_147_0
Gabriele Nebe; Elisabeth Nossek; Boris Venkov. Low dimensional strongly perfect lattices. II: Dual strongly perfect lattices of dimension 13 and 15.. Journal de théorie des nombres de Bordeaux, Volume 25 (2013) no. 1, pp. 147-161. doi : 10.5802/jtnb.830. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.830/
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