Geodesic
On a class of perfect codes with maximum components
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 645-655.

Voir la notice de l'article provenant de la source Math-Net.Ru

We show the existence of a wide class of binary extended perfect Solov'eva codes of length 16 with $ij$-components of maximum size.
Keywords: perfect binary codes, component. 
@article{SEMR_2016_13_a62,
     author = {I. Yu. Mogilnykh and F. I. Solov'eva},
     title = {On a class of perfect codes with maximum components},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {645--655},
     publisher = {mathdoc},
     volume = {13},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2016_13_a62/}
}
TY  - JOUR
AU  - I. Yu. Mogilnykh
AU  - F. I. Solov'eva
TI  - On a class of perfect codes with maximum components
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2016
SP  - 645
EP  - 655
VL  - 13
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2016_13_a62/
LA  - ru
ID  - SEMR_2016_13_a62
ER  - 
%0 Journal Article
%A I. Yu. Mogilnykh
%A F. I. Solov'eva
%T On a class of perfect codes with maximum components
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2016
%P 645-655
%V 13
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2016_13_a62/
%G ru
%F SEMR_2016_13_a62
I. Yu. Mogilnykh; F. I. Solov'eva. On a class of perfect codes with maximum components. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 645-655. http://geodesic.mathdoc.fr/item/SEMR_2016_13_a62/

[1] F. I. Solov'eva, “Switching Methods for Error-Correcting Codes”, Aspects of Network and Information Security, NATO Science for Peace and Security, Series D: Information and Communication Security, 17, IOS Press, 2008, 333–342

[2] F. I. Solov'eva, “A survey on perfect codes”, Matematicheskie voprosi kibrenetiki, 18, 2013, 5–34 (in Russian)

[3] F. I. Solov'eva, Exact Bounds on the Connectivity of Code-Generated Disjunctive Normal Forms, Preprint No 10, Inst. Math. of the Siberian Branch of Acad. of Sciences, USSR, 1990

[4] F. I. Solov'eva, “Factorization of code generating d.n.f.”, Methody Diskr. Analiza, 47 (1988), 66–88 (in Russian) | MR | Zbl

[5] S. V. Avgustinovich, F. I. Solov'eva, “On projections of perfect binary codes”, Proc. Seventh Joint Swedish-Russian Int. Workshop on Inform. Theory (St.-Petersburg, Russia, 1995), 25–26

[6] F. I. Solov'eva, “Structure of i-components of perfect binary codes”, Discrete Appl. Math., 111:1–2 (2001), 189–197 | DOI | MR | Zbl

[7] P. R. J. Östergård, O. Pottonen, “The perfect binary one-error-correcting codes of length 15. Part I: Classification”, IEEE Trans. Inform. Theory, 55 (2009), 4657–4660 | DOI | MR

[8] P. R. J. Östergård, K. T. Phelps, O. Pottonen, “The perfect binary one-error-correcting codes of length 15. Part II: Properties”, IEEE Trans. Inform. Theory, 56:6 (2010), 2571–2582 | DOI | MR

[9] O. Pottonen, Private communication

[10] V. N. Potapov, “Cardinality spectra of components of correlation immune functions, bent functions, perfect colorings, and codes”, Probl. of Inform. Transm., 48:1 (2012), 47–55 | DOI | MR | Zbl

[11] K. T. Phelps, M. LeVan, “Switching equivalence classes of perfect codes”, Des., Codes and Cryptogr., 56:2 (1999), 179–184 | DOI | MR

[12] F. I. Solov'eva, “On binary nongroup codes”, Methody Diskr. Analiza, 37 (1981), 65–76 (in Russian) | MR | Zbl

[13] F. J. MacWilliams, N. J. A. Sloane, The Theory of Error-Correcting Codes, North Holland, 1977 | MR | Zbl

[14] D. S. Krotov, “A Partition of the hypercube into Maximally Nonparallel Hamming Codes”, Journal of Combinatorial Designs, 22 (2014), 179–187 | DOI | MR | Zbl

[15] K. T. Phelps, “An enumeration of 1-perfect binary codes of length 15”, Australian Journal of Combinatorics, 21 (2000), 287–298 | MR | Zbl

[16] P. Delsarte, “An algebraic approach to association schemes of coding theory”, Philips J. Res., 10 (1973), 1–97 | MR