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The classification of complementary information set codes of lengths $14$ and $16$
New nonexistence results for spherical designs
1. | Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 8 G.Bonchev str., 1113 Sofia, Bulgaria |
2. | Faculty of Mathematics and Informatics, Sofia University, 5 James Bourchier blvd, 1164 Sofia, Bulgaria |
References:
[1] |
M. Abramowitz and I. Stegun, "Handbook of Mathematical Functions,'' Dover, New York, 1965. |
[2] |
B. Bajnok, Constructions of spherical 3-designs, Des. Codes Crypt., 21 (2000), 11-18.
doi: 10.1023/A:1008367006853. |
[3] |
S. Boumova, P. Boyvalenkov and D. Danev, Necessary conditions for existence of some designs in polynomial metric spaces, Europ. J. Combin., 20 (1999), 213-225.
doi: 10.1006/eujc.1998.0278. |
[4] |
S. Boumova, P. Boyvalenkov and D. Danev, New nonexistence results for spherical designs, in "Constructive Theory of Functions'' (ed. B. Bojanov), Darba, Sofia, (2003), 225-232. |
[5] |
S. Boumova, P. Boyvalenkov, H. Kulina and M. Stoyanova, Polynomial techniques for investigation of spherical designs, Des. Codes Crypt., 51 (2009), 275-288.
doi: 10.1007/s10623-008-9260-0. |
[6] |
S. Boumova, P. Boyvalenkov and M. Stoyanova, A method for proving nonexistence of spherical designs of odd strength and odd cardinality, Probl. Inform. Transm., 45 (2009), 110-123; translated from: Probl. Pered. Inform., 45 (2009), 41-55.
doi: 10.1134/S0032946009020033. |
[7] |
S. Boumova and D. Danev, On the asymptotic behaviour of a necessary condition for existence of spherical designs, in "Proc. Intern. Workshop ACCT,'' (2002), 54-57. |
[8] |
P. Boyvalenkov, D. Danev and S. Nikova, Nonexistence of certain spherical designs of odd strengths and cardinalities, Discr. Comp. Geom., 21 (1999), 143-156.
doi: 10.1007/PL00009406. |
[9] |
P. Boyvalenkov and M. Stoyanova, A new asymptotic bound of the minimum possible odd cardinality of spherical $(2k-1)$-designs, Discrete Math., 310 (2010), 2170-2175.
doi: 10.1016/j.disc.2010.04.007. |
[10] |
P. Delsarte, J.-M. Goethals and J. J. Seidel, Spherical codes and designs, Geom. Dedicata, 6 (1977), 363-388. |
[11] |
V. I. Levenshtein, Universal bounds for codes and designs, in "Handbook of Coding Theory'' (eds. V. Pless and W.C. Huffman), Elsevier, (1998), 499-648. |
[12] |
show all references
References:
[1] |
M. Abramowitz and I. Stegun, "Handbook of Mathematical Functions,'' Dover, New York, 1965. |
[2] |
B. Bajnok, Constructions of spherical 3-designs, Des. Codes Crypt., 21 (2000), 11-18.
doi: 10.1023/A:1008367006853. |
[3] |
S. Boumova, P. Boyvalenkov and D. Danev, Necessary conditions for existence of some designs in polynomial metric spaces, Europ. J. Combin., 20 (1999), 213-225.
doi: 10.1006/eujc.1998.0278. |
[4] |
S. Boumova, P. Boyvalenkov and D. Danev, New nonexistence results for spherical designs, in "Constructive Theory of Functions'' (ed. B. Bojanov), Darba, Sofia, (2003), 225-232. |
[5] |
S. Boumova, P. Boyvalenkov, H. Kulina and M. Stoyanova, Polynomial techniques for investigation of spherical designs, Des. Codes Crypt., 51 (2009), 275-288.
doi: 10.1007/s10623-008-9260-0. |
[6] |
S. Boumova, P. Boyvalenkov and M. Stoyanova, A method for proving nonexistence of spherical designs of odd strength and odd cardinality, Probl. Inform. Transm., 45 (2009), 110-123; translated from: Probl. Pered. Inform., 45 (2009), 41-55.
doi: 10.1134/S0032946009020033. |
[7] |
S. Boumova and D. Danev, On the asymptotic behaviour of a necessary condition for existence of spherical designs, in "Proc. Intern. Workshop ACCT,'' (2002), 54-57. |
[8] |
P. Boyvalenkov, D. Danev and S. Nikova, Nonexistence of certain spherical designs of odd strengths and cardinalities, Discr. Comp. Geom., 21 (1999), 143-156.
doi: 10.1007/PL00009406. |
[9] |
P. Boyvalenkov and M. Stoyanova, A new asymptotic bound of the minimum possible odd cardinality of spherical $(2k-1)$-designs, Discrete Math., 310 (2010), 2170-2175.
doi: 10.1016/j.disc.2010.04.007. |
[10] |
P. Delsarte, J.-M. Goethals and J. J. Seidel, Spherical codes and designs, Geom. Dedicata, 6 (1977), 363-388. |
[11] |
V. I. Levenshtein, Universal bounds for codes and designs, in "Handbook of Coding Theory'' (eds. V. Pless and W.C. Huffman), Elsevier, (1998), 499-648. |
[12] |
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