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On the functional codes arising from the intersections of algebraic hypersurfaces of small degree with a non-singular quadric
On the dual code of points and generators on the Hermitian variety $\mathcal{H}(2n+1,q^{2})$
1. | UGent, Department of Mathematics, Krijgslaan 281-S22, 9000 Gent, Flanders, Belgium, Belgium |
References:
[1] |
E. F. Assmus and J. D. Key, Designs and their Codes, Cambridge University Press, Cambridge, 1992. |
[2] |
S. V. Droms, K. E. Mellinger and C. Meyer, LDPC codes generated by conics in the classical projective plane, Des. Codes Cryptogr., 40 (2006), 343-356.
doi: 10.1007/s10623-006-0022-6. |
[3] |
Y. Fujiwara, D. Clark, P. Vandendriessche, M. De Boeck and V. D. Tonchev, Entanglement-assisted quantum low-density parity-check codes, Phys. Rev. A, 82 (2010), 042338.
doi: 10.1103/PhysRevA.82.042338. |
[4] |
J. W. P. Hirschfeld and J. A. Thas, General Galois Geometries, Oxford University Press, Oxford, 1991. |
[5] |
J.-L. Kim, K. Mellinger and L. Storme, Small weight codewords in LDPC codes defined by (dual) classical generalised quadrangles, Des. Codes Cryptogr., 42 (2007), 73-92.
doi: 10.1007/s10623-006-9017-6. |
[6] |
A. Klein, K. Metsch and L. Storme, Small maximal partial spreads in classical finite polar spaces, Adv. Geom., 10 (2010), 379-402.
doi: 10.1515/ADVGEOM.2010.007. |
[7] |
M. Lavrauw, L. Storme and G. Van de Voorde, Linear codes from projective spaces, in Error-Correcting Codes, Finite Geometries, and Cryptography (eds. A.A. Bruen and D.L. Wehlau), 2010, 185-202.
doi: 10.1090/conm/523/10326. |
[8] |
V. Pepe, L. Storme and G. Van de Voorde, On codewords in the dual code of classical generalised quadrangles and classical polar spaces, Discrete Math., 310 (2010), 3132-3148.
doi: 10.1016/j.disc.2009.06.010. |
[9] |
P. Vandendriessche, LDPC codes associated with linear representations of geometries, Adv. Math. Commun., 4 (2010), 405-417.
doi: 10.3934/amc.2010.4.405. |
[10] |
P. Vandendriessche, Some low-density parity-check codes derived from finite geometries, Des. Codes. Cryptogr., 54 (2010), 287-297.
doi: 10.1007/s10623-009-9324-9. |
show all references
References:
[1] |
E. F. Assmus and J. D. Key, Designs and their Codes, Cambridge University Press, Cambridge, 1992. |
[2] |
S. V. Droms, K. E. Mellinger and C. Meyer, LDPC codes generated by conics in the classical projective plane, Des. Codes Cryptogr., 40 (2006), 343-356.
doi: 10.1007/s10623-006-0022-6. |
[3] |
Y. Fujiwara, D. Clark, P. Vandendriessche, M. De Boeck and V. D. Tonchev, Entanglement-assisted quantum low-density parity-check codes, Phys. Rev. A, 82 (2010), 042338.
doi: 10.1103/PhysRevA.82.042338. |
[4] |
J. W. P. Hirschfeld and J. A. Thas, General Galois Geometries, Oxford University Press, Oxford, 1991. |
[5] |
J.-L. Kim, K. Mellinger and L. Storme, Small weight codewords in LDPC codes defined by (dual) classical generalised quadrangles, Des. Codes Cryptogr., 42 (2007), 73-92.
doi: 10.1007/s10623-006-9017-6. |
[6] |
A. Klein, K. Metsch and L. Storme, Small maximal partial spreads in classical finite polar spaces, Adv. Geom., 10 (2010), 379-402.
doi: 10.1515/ADVGEOM.2010.007. |
[7] |
M. Lavrauw, L. Storme and G. Van de Voorde, Linear codes from projective spaces, in Error-Correcting Codes, Finite Geometries, and Cryptography (eds. A.A. Bruen and D.L. Wehlau), 2010, 185-202.
doi: 10.1090/conm/523/10326. |
[8] |
V. Pepe, L. Storme and G. Van de Voorde, On codewords in the dual code of classical generalised quadrangles and classical polar spaces, Discrete Math., 310 (2010), 3132-3148.
doi: 10.1016/j.disc.2009.06.010. |
[9] |
P. Vandendriessche, LDPC codes associated with linear representations of geometries, Adv. Math. Commun., 4 (2010), 405-417.
doi: 10.3934/amc.2010.4.405. |
[10] |
P. Vandendriessche, Some low-density parity-check codes derived from finite geometries, Des. Codes. Cryptogr., 54 (2010), 287-297.
doi: 10.1007/s10623-009-9324-9. |
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