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 $n>20^{10}-1$ of complete rank with kernels of all possible dimensions $K$ from $(n-1)/2$ to $U(n)$, which is the maximum possible. For every $k\in \{(n-1)/2,\dots,U(n)-2\}$, we construct such codes of length $n,31\leqslant n\leqslant 2^{10}-1$. 
@article{DA_2001_8_4_a0,
     author = {S. V. Avgustinovich and F. I. Solov'eva and O. Heden},
     title = {Perfect codes of complete rank with kernels of large dimensions},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {3--8},
     publisher = {mathdoc},
     volume = {8},
     number = {4},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2001_8_4_a0/}
}
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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. http://geodesic.mathdoc.fr/item/DA_2001_8_4_a0/