Voir la notice de l'article provenant de la source Math-Net.Ru
@article{MZM_2000_68_4_a0, author = {V. V. Arestov and A. G. Babenko}, title = {Estimates of the maximal value of angular code distance for 24 and~25 points on the unit sphere in~$\mathbb R^4$}, journal = {Matemati\v{c}eskie zametki}, pages = {483--503}, publisher = {mathdoc}, volume = {68}, number = {4}, year = {2000}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/MZM_2000_68_4_a0/} }
TY - JOUR AU - V. V. Arestov AU - A. G. Babenko TI - Estimates of the maximal value of angular code distance for 24 and~25 points on the unit sphere in~$\mathbb R^4$ JO - Matematičeskie zametki PY - 2000 SP - 483 EP - 503 VL - 68 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/MZM_2000_68_4_a0/ LA - ru ID - MZM_2000_68_4_a0 ER -
%0 Journal Article %A V. V. Arestov %A A. G. Babenko %T Estimates of the maximal value of angular code distance for 24 and~25 points on the unit sphere in~$\mathbb R^4$ %J Matematičeskie zametki %D 2000 %P 483-503 %V 68 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/MZM_2000_68_4_a0/ %G ru %F MZM_2000_68_4_a0
V. V. Arestov; A. G. Babenko. Estimates of the maximal value of angular code distance for 24 and~25 points on the unit sphere in~$\mathbb R^4$. Matematičeskie zametki, Tome 68 (2000) no. 4, pp. 483-503. http://geodesic.mathdoc.fr/item/MZM_2000_68_4_a0/
[1] Mackay A. L., “The packing of three-dimensional spheres on surface of a four-dimensional hypersphere”, J. Phys. A: Math. Gen., 13 (1980), 3373–3379 | DOI | MR | Zbl
[2] Kokster G. S. M., Vvedenie v geometriyu, Nauka, M., 1966
[3] Odlyzko A. M., Sloane N. J. A., “New bounds on the number of unit spheres that can touch a unit sphere in $n$ dimensions”, J. of Combin. Theory Ser. A, 26:2 (1979), 210–214 | DOI | MR | Zbl
[4] Delsarte Ph., “Bounds for unrestricted codes, by linear programming”, Philips Res. Rep., 27 (1972), 272–289 | MR | Zbl
[5] Delsart F., Algebraicheskii podkhod k skhemam otnoshenii teorii kodirovaniya, Mir, M., 1976
[6] Delsarte P., Goethalts J. M., Seidel J. J., “Spherical codes and designs”, Geom. Dedicata, 6 (1977), 363–388 | MR | Zbl
[7] Kabatyanskii G. A., Levenshtein V. I., “O granitsakh dlya upakovok na sfere i v prostranstve”, Problemy peredachi informatsii, 14:1 (1978), 3–25 | MR | Zbl
[8] Arestov V. V., Babenko A. G., “O skheme Delsarta otsenki kontaktnykh chisel”, Tr. MIAN, 219, Nauka, M., 1997, 44–73 | MR | Zbl
[9] Konvei Dzh., Sloen N., Upakovki sharov, reshetki i gruppy, T. 1, 2, Mir, M., 1990
[10] Conway J. H., Sloane N. J. A., Sphere Packings, Lattices and Groups, Second Edition, Springer-Verlag, New York, 1993 | Zbl
[11] Conway J. H., Sloane N. J. A., Sphere Packings, Lattices and Groups, Third Edition, Springer-Verlag, New York, 1998
[12] Rankin R. A., “The closest packing of spherical caps in $n$ dimensions”, Proc. Glasgow Math. Assoc., 2 (1955), 139–144 | DOI | MR | Zbl
[13] Levenshtein V. I., “O granitsakh dlya upakovok v $n$-mernom evklidovom prostranstve”, Dokl. AN SSSR, 245 (1979), 1299–1303 | MR
[14] Sidelnikov V. M., “Ob ekstremalnykh mnogochlenakh, ispolzuemykh pri otsenkakh moschnosti koda”, Problemy peredachi informatsii, 16:3 (1980), 17–30 | MR | Zbl
[15] Bannai E., Sloane N. J. A., “Uniqueness of certain spherical codes”, Canad. J. Math., 33 (1981), 437–449 | MR
[16] Levenshtein V. I., “Granitsy dlya upakovok metricheskikh prostranstv i nekotorye ikh prilozheniya”, Problemy kibernetiki, 40 (1983), 44–110
[17] Yudin V. A., “Minimum potentsialnoi energii tochechnoi sistemy zaryadov”, Diskretnaya matem., 4:2 (1992), 115–121 | MR
[18] Boyvalenkov P., “Extremal polynomials for obtaining bounds for spherical codes and designs”, Discrete Comput. Geom., 14 (1995), 167–183 | DOI | MR | Zbl
[19] Boyvalenkov P. G., Danev D. P., Bumova S. P., “Upper bounds on the minimum distance of spherical codes”, IEEE Trans. Inform. Theory, 42:5 (1996), 1576–1581 | DOI | MR | Zbl
[20] Boyvalenkov P., “On the upper bounds for the kissing numbers”, Serdica, 18 (1992), 278–285 | MR | Zbl
[21] Boyvalenkov P., “On the extremality of the polynomials used for obtaining the best known upper bounds for the kissing numbers”, J. Geom., 49 (1994), 67–71 | DOI | MR | Zbl
[22] Hardin R. H., Sloane N. J. A., Smith W. D., Spherical codes, http://www.research.att.com/\allowbreakñjas/packings/index.html
[23] Galiev Sh. I., “Mnogokratnye upakovki i pokrytiya sfery”, Diskretnaya matem., 8:3 (1996), 148–160 | MR | Zbl
[24] Pashkovskii S., Vychislitelnye primeneniya mnogochlenov i ryadov Chebysheva, Nauka, M., 1983