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The minimum order of complete caps in $PG(4,4)$
1. | Department of Mathematics and Informatics, Perugia University, Perugia, 06123, Italy, Italy, Italy |
2. | Institute for Information Transmission Problems (Kharkevich institute), Russian Academy of Sciences, GSP-4, Moscow, 127994, Russian Federation |
References:
[1] |
D. Bartoli, "Quantum Codes and Related Geometric Properties,'' Ph.D thesis, Università degli Studi di Perugia, Perugia, Italy, 2008. |
[2] |
D. Bartoli, J. Bierbrauer, S. Marcugini and F. Pambianco, Geometric constructions of quantum codes, in "Error-Correcting Codes, Finite Geometries and Cryptography'' (eds. A.A. Bruen and D.L. Wehlau), AMS, (2010), 149-154. |
[3] |
D. Bartoli, S. Marcugini and F. Pambianco, A computer based classification of caps in $PG(3,4)$, in "Rapporto Tecnico - 8/2009,'' Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Perugia, Italy, (2009). |
[4] |
D. Bartoli, S. Marcugini and F. Pambianco, New quantum caps in $PG(4,4)$,, submitted., ().
|
[5] |
J. Bierbrauer, "Introduction to Coding Theory,'' Chapman and Hall/CRC, Boca Raton, 2005. |
[6] |
J. Bierbrauer, G. Faina, M. Giulietti, S. Marcugini and F. Pambianco, The geometry of quantum codes, Innov. Incidence Geom., 6 (2009), 53-71. |
[7] |
J. Bierbrauer, S. Marcugini and F. Pambianco, The smallest size of a complete cap in $PG(3,7)$, Discrete Math., 306 (2006), 1257-1263.
doi: 10.1016/j.disc.2005.06.039. |
[8] |
A. Davydov, G. Faina, S. Marcugini and F. Pambianco, On size of complete caps in projective spaces $PG(n,q)$ and arcs in planes $PG(2,q)$, J. Geom., 94 (2009), 31-58.
doi: 10.1007/s00022-009-0009-3. |
[9] |
A. A. Davydov, S. Marcugini and F. Pambianco, Complete caps in projective spaces $PG(n,q)$, J. Geom., 80 (2004), 23-30.
doi: 10.1007/s00022-004-1778-3. |
[10] |
G. Faina and F. Pambianco, On the spectrum of the values $k$ for which a complete $k$-cap in $PG(n,q)$ exists, J. Geom., 62 (1998), 84-98.
doi: 10.1007/BF01237602. |
[11] |
M. Grassl, Bounds on the minimum distance of linear codes,, available online at \url{http://www.codetables.de}, ().
|
[12] |
R. Hill, Caps and codes, Discrete Math., 22 (1978), 111-137.
doi: 10.1016/0012-365X(78)90120-6. |
[13] |
S. Marcugini, A. Milani and F. Pambianco, Complete arcs in $PG(2,25)$: the spectrum of the sizes and the classification of the smallest complete arcs, Discrete Math., 307 (2007), 739-747.
doi: 10.1016/j.disc.2005.11.094. |
[14] |
F. Pambianco and L. Storme, Small complete caps in spaces of even characteristic, J. Combin. Theory Ser. A, 75 (1996), 70-84.
doi: 10.1006/jcta.1996.0064. |
show all references
References:
[1] |
D. Bartoli, "Quantum Codes and Related Geometric Properties,'' Ph.D thesis, Università degli Studi di Perugia, Perugia, Italy, 2008. |
[2] |
D. Bartoli, J. Bierbrauer, S. Marcugini and F. Pambianco, Geometric constructions of quantum codes, in "Error-Correcting Codes, Finite Geometries and Cryptography'' (eds. A.A. Bruen and D.L. Wehlau), AMS, (2010), 149-154. |
[3] |
D. Bartoli, S. Marcugini and F. Pambianco, A computer based classification of caps in $PG(3,4)$, in "Rapporto Tecnico - 8/2009,'' Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Perugia, Italy, (2009). |
[4] |
D. Bartoli, S. Marcugini and F. Pambianco, New quantum caps in $PG(4,4)$,, submitted., ().
|
[5] |
J. Bierbrauer, "Introduction to Coding Theory,'' Chapman and Hall/CRC, Boca Raton, 2005. |
[6] |
J. Bierbrauer, G. Faina, M. Giulietti, S. Marcugini and F. Pambianco, The geometry of quantum codes, Innov. Incidence Geom., 6 (2009), 53-71. |
[7] |
J. Bierbrauer, S. Marcugini and F. Pambianco, The smallest size of a complete cap in $PG(3,7)$, Discrete Math., 306 (2006), 1257-1263.
doi: 10.1016/j.disc.2005.06.039. |
[8] |
A. Davydov, G. Faina, S. Marcugini and F. Pambianco, On size of complete caps in projective spaces $PG(n,q)$ and arcs in planes $PG(2,q)$, J. Geom., 94 (2009), 31-58.
doi: 10.1007/s00022-009-0009-3. |
[9] |
A. A. Davydov, S. Marcugini and F. Pambianco, Complete caps in projective spaces $PG(n,q)$, J. Geom., 80 (2004), 23-30.
doi: 10.1007/s00022-004-1778-3. |
[10] |
G. Faina and F. Pambianco, On the spectrum of the values $k$ for which a complete $k$-cap in $PG(n,q)$ exists, J. Geom., 62 (1998), 84-98.
doi: 10.1007/BF01237602. |
[11] |
M. Grassl, Bounds on the minimum distance of linear codes,, available online at \url{http://www.codetables.de}, ().
|
[12] |
R. Hill, Caps and codes, Discrete Math., 22 (1978), 111-137.
doi: 10.1016/0012-365X(78)90120-6. |
[13] |
S. Marcugini, A. Milani and F. Pambianco, Complete arcs in $PG(2,25)$: the spectrum of the sizes and the classification of the smallest complete arcs, Discrete Math., 307 (2007), 739-747.
doi: 10.1016/j.disc.2005.11.094. |
[14] |
F. Pambianco and L. Storme, Small complete caps in spaces of even characteristic, J. Combin. Theory Ser. A, 75 (1996), 70-84.
doi: 10.1006/jcta.1996.0064. |
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