Geodesic
A lower bound for the number of transitive perfect codes
Diskretnyj analiz i issledovanie operacij, Tome 13 (2006) no. 4, pp. 49-59

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We construct at least $\dfrac1{8n^2\sqrt3}e^{\pi\sqrt{2n/3}}(1+o(1))$ pairwise nonequivalent transitive extended perfect codes of length $4n$ as $n\to\infty$. 
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     author = {V. N. Potapov},
     title = {A lower bound for the number of transitive perfect codes},
     journal = {Diskretnyj analiz i issledovanie operacij},
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     publisher = {mathdoc},
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     year = {2006},
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     url = {http://geodesic.mathdoc.fr/item/DA_2006_13_4_a4/}
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V. N. Potapov. A lower bound for the number of transitive perfect codes. Diskretnyj analiz i issledovanie operacij, Tome 13 (2006) no. 4, pp. 49-59. http://geodesic.mathdoc.fr/item/DA_2006_13_4_a4/