Geodesic
On partitions into affine nonequivalent perfect $q$-ary codes
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 7 (2010), pp. 425-434.

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It is proved that there exists a partition of the set $F^N_q$ of all $q$-ary vectors of length $N$ into pairwise affine nonequivalent perfect $q$-ary codes of length $N$ with the Hamming distance $3$ for any $N=(q^m-1)/(q-1)$, where $q=p^r,$ $p$ is prime.
Keywords: perfect $q$-ary code, partition into perfect codes, switching
Mots-clés : affine nonequivalence of codes. 
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A. V. Los'; F. I. Solov'eva. On partitions into affine nonequivalent perfect $q$-ary codes. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 7 (2010), pp. 425-434. http://geodesic.mathdoc.fr/item/SEMR_2010_7_a26/

[1] Avgustinovich S. V., Soloveva F. I., Kheden U., “O razbieniyakh $n$-kuba na neekvivalentnye sovershennye kody”, Probl. peredachi inform., 43:4 (2007), 45–50 | MR | Zbl

[2] Cohen G., Honkala I., Lobstein A., Litsyn S., Covering codes, Elsevier, 1998 | MR

[3] Schönheim J., “On linear and nonlinear single-error-correcting $q$-nary $1$ perfect codes”, Inform. Control, 12 (1986), 23–26 | DOI | MR

[4] Phelps K. T., Villanueva M., “Ranks of $q$-ary 1 perfect codes”, Des. Codes Cryptogr., 27 (2002), 139–144 | DOI | MR | Zbl

[5] Mak-Vilyams F. Dzh., Sloen N. Dzh. A., Teoriya kodov, ispravlyayuschikh oshibki, M., 1979

[6] Avgustinovich S. V., Soloveva F. I., “Postroenie sovershennykh dvoichnykh kodov posledovatelnymi sdvigami $\widetilde{\alpha}$-komponent”, Probl. peredachi inform., 33:3 (1997), 15–21 | MR | Zbl

[7] Los A. V., “Postroenie sovershennykh $q$-znachnykh kodov posledovatelnymi sdvigami $\widetilde{\alpha}$-komponent”, Probl. peredachi inform., 40:1 (2004), 33–39 | MR | Zbl

[8] Los A. V., “Postroenie sovershennykh $q$-znachnykh kodov svitchingami prostykh komponent”, Probl. peredachi inform., 42:1 (2006), 34–42 | MR | Zbl