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On the structure of non-full-rank perfect $q$-ary codes
A geometric proof of the upper bound on the size of partial spreads in $H(4n+1,$q2$)$
1. | Department of Mathematics, Ghent University, Krijgslaan 281, S22, B-9000 Ghent, Belgium |
References:
[1] |
A. Aguglia, A. Cossidente and G. L. Ebert, Complete spans on Hermitian varieties, Des. Codes Cryptogr., 29 (2003), 7-15.
doi: 10.1023/A:1024179703511. |
[2] |
J. De Beule, A. Klein, K. Metsch and L. Storme, Partial ovoids and partial spreads in Hermitian polar spaces, Des. Codes Cryptogr., 47 (2008), 21-34.
doi: 10.1007/s10623-007-9047-8. |
[3] |
J. De Beule and K. Metsch, The maximum size of a partial spread in $H(5,q^2)$ is $q^3+1$, J. Combin. Theory Ser. A, 114 (2007), 761-768.
doi: 10.1016/j.jcta.2006.08.005. |
[4] |
J. W. P. Hirschfeld and J. A. Thas, "General Galois Geometries,'' The Clarendon Press, Oxford University Press, New York, 1991. |
[5] |
D. Luyckx, On maximal partial spreads of $H(2n+1,q^2)$, Discrete Math., 308 (2008), 375-379.
doi: 10.1016/j.disc.2006.11.051. |
[6] |
J. A. Thas, Old and new results on spreads and ovoids of finite classical polar spaces, Ann. Discrete Math., 52 (1992), 529-544.
doi: 10.1016/S0167-5060(08)70936-1. |
[7] |
F. Vanhove, The maximum size of a partial spread in $H(4n+1,q^2)$ is q2n+1$+1$, Electron. J. Combin., 16 (2009), 1-6. |
show all references
References:
[1] |
A. Aguglia, A. Cossidente and G. L. Ebert, Complete spans on Hermitian varieties, Des. Codes Cryptogr., 29 (2003), 7-15.
doi: 10.1023/A:1024179703511. |
[2] |
J. De Beule, A. Klein, K. Metsch and L. Storme, Partial ovoids and partial spreads in Hermitian polar spaces, Des. Codes Cryptogr., 47 (2008), 21-34.
doi: 10.1007/s10623-007-9047-8. |
[3] |
J. De Beule and K. Metsch, The maximum size of a partial spread in $H(5,q^2)$ is $q^3+1$, J. Combin. Theory Ser. A, 114 (2007), 761-768.
doi: 10.1016/j.jcta.2006.08.005. |
[4] |
J. W. P. Hirschfeld and J. A. Thas, "General Galois Geometries,'' The Clarendon Press, Oxford University Press, New York, 1991. |
[5] |
D. Luyckx, On maximal partial spreads of $H(2n+1,q^2)$, Discrete Math., 308 (2008), 375-379.
doi: 10.1016/j.disc.2006.11.051. |
[6] |
J. A. Thas, Old and new results on spreads and ovoids of finite classical polar spaces, Ann. Discrete Math., 52 (1992), 529-544.
doi: 10.1016/S0167-5060(08)70936-1. |
[7] |
F. Vanhove, The maximum size of a partial spread in $H(4n+1,q^2)$ is q2n+1$+1$, Electron. J. Combin., 16 (2009), 1-6. |
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