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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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/

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