Geodesic
Perfect codes of complete rank with kernels of large dimensions
Diskretnyj analiz i issledovanie operacij, Tome 8 (2001) no. 4, pp. 3-8.

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We construct perfect codes of all admissible lengths n>2010−1 of complete rank with kernels of all possible dimensions K from (n−1)/2 to U(n), which is the maximum possible. For every k∈{(n−1)/2,…,U(n)−2}, we construct such codes of length n,31⩽n⩽210−1. 
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     title = {Perfect codes of complete rank with kernels of large dimensions},
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S. V. Avgustinovich; F. I. Solov'eva; O. Heden. Perfect codes of complete rank with kernels of large dimensions. Diskretnyj analiz i issledovanie operacij, Tome 8 (2001) no. 4, pp. 3-8. https://geodesic-test.mathdoc.fr/item/DA_2001_8_4_a0/