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On the dual code of points and generators on the Hermitian variety $\mathcal{H}(2n+1,q^{2})$
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Higher genus universally decodable matrices (UDMG)
On the functional codes arising from the intersections of algebraic hypersurfaces of small degree with a non-singular quadric
1. | Dipartimento di Matematica ed Informatica, Università degli Studi di Perugia, Via Vanvitelli 1, 06123 Perugia, Italy |
2. | Department of Mathematics, Ghent University, Krijgslaan 281 - S22, 9000 Ghent |
References:
[1] |
D. Bartoli, M. De Boeck, S. Fanali and L. Storme, On the functional codes defined by quadrics and Hermitian varieties, Des. Codes Cryptogr., 71 (2014), 21-46.
doi: 10.1007/s10623-012-9712-4. |
[2] |
A. Cafure and G. Matera, Improved explicit estimates on the number of solutions of equations over a finite field, Finite Fields Appl., 12 (2006), 155-185.
doi: 10.1016/j.ffa.2005.03.003. |
[3] |
F. A. B. Edoukou, A. Hallez, F. Rodier and L. Storme, A study of intersections of quadrics having applications on the small weight codewords of the functional codes $C_2(Q)$, $Q$ a non-singular quadric, J. Pure Appl. Algebra, 214 (2010), 1729-1739.
doi: 10.1016/j.jpaa.2009.12.017. |
[4] |
F. A. B. Edoukou, A. Hallez, F. Rodier and L. Storme, On the small weight codewords of the functional codes $C_{herm}(X)$, $X$ a non-singular Hermitian variety, Des. Codes Cryptogr., 56 (2010), 219-233.
doi: 10.1007/s10623-010-9401-0. |
[5] |
A. Hallez and L. Storme, Functional codes arising from quadric intersections with Hermitian varieties, Finite Fields Appl., 16 (2010), 27-35.
doi: 10.1016/j.ffa.2009.11.005. |
[6] |
J. W. P. Hirschfeld and J. A. Thas, General Galois Geometries, The Clarendon Press, Oxford University Press, 1991. |
[7] |
G. Lachaud, Number of points of plane sections and linear codes defined on algebraic varieties, in Arithmetic, Geometry, and Coding Theory, Walter De Gruyter, Berlin, 1996, 77-104. |
show all references
References:
[1] |
D. Bartoli, M. De Boeck, S. Fanali and L. Storme, On the functional codes defined by quadrics and Hermitian varieties, Des. Codes Cryptogr., 71 (2014), 21-46.
doi: 10.1007/s10623-012-9712-4. |
[2] |
A. Cafure and G. Matera, Improved explicit estimates on the number of solutions of equations over a finite field, Finite Fields Appl., 12 (2006), 155-185.
doi: 10.1016/j.ffa.2005.03.003. |
[3] |
F. A. B. Edoukou, A. Hallez, F. Rodier and L. Storme, A study of intersections of quadrics having applications on the small weight codewords of the functional codes $C_2(Q)$, $Q$ a non-singular quadric, J. Pure Appl. Algebra, 214 (2010), 1729-1739.
doi: 10.1016/j.jpaa.2009.12.017. |
[4] |
F. A. B. Edoukou, A. Hallez, F. Rodier and L. Storme, On the small weight codewords of the functional codes $C_{herm}(X)$, $X$ a non-singular Hermitian variety, Des. Codes Cryptogr., 56 (2010), 219-233.
doi: 10.1007/s10623-010-9401-0. |
[5] |
A. Hallez and L. Storme, Functional codes arising from quadric intersections with Hermitian varieties, Finite Fields Appl., 16 (2010), 27-35.
doi: 10.1016/j.ffa.2009.11.005. |
[6] |
J. W. P. Hirschfeld and J. A. Thas, General Galois Geometries, The Clarendon Press, Oxford University Press, 1991. |
[7] |
G. Lachaud, Number of points of plane sections and linear codes defined on algebraic varieties, in Arithmetic, Geometry, and Coding Theory, Walter De Gruyter, Berlin, 1996, 77-104. |
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