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A note on the minimum Lee distance of certain self-dual modular codes
Singularities of symmetric hypersurfaces and Reed-Solomon codes
1. | Instituto del Desarrollo Humano, Universidad Nacional de General Sarmiento, J.M. Gutiérrez 1150, Los Polvorines (B1613GSX) Buenos Aires, Argentina, and, Ciclo Básico Común, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón III (1428) Buenos Aires, Argentina, and, National Council of Research and Technology (CONICET), Buenos Aires, Argentina |
2. | Instituto del Desarrollo Humano, Universidad Nacional de General Sarmiento, J.M. Gutiérrez 1150, Los Polvorines (B1613GSX) Buenos Aires, Argentina, and, National Council of Research and Technology (CONICET), Buenos Aires, Argentina, Argentina |
References:
[1] |
A. Adolphson and S. Sperber, On the degree of the L-function associated with an exponential sum,, Compos. Math., 68 (1988), 125.
|
[2] |
Y. Aubry and F. Rodier, Differentially 4-uniform functions,, in, (2010), 1.
|
[3] |
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.
doi: 10.1016/j.ffa.2005.03.003. |
[4] |
Q. Cheng and E. Murray, On deciding deep holes of Reed-Solomon codes,, in, (2007), 296.
doi: 10.1007/978-3-540-72504-6_27. |
[5] |
R. Coulter and M. Henderson, A note on the roots of trinomials over a finite field,, Bull. Austral. Math. Soc., 69 (2004), 429.
doi: 10.1017/S0004972700036200. |
[6] |
T. Ernst, Generalized Vandermonde determinants,, report 2000: 6 Matematiska Institutionen, (2000). Google Scholar |
[7] |
D. K. Faddeev and I. S. Sominskii, "Problems in Higher Algebra,", Freeman, (1965).
|
[8] |
S. Ghorpade and G. Lachaud, Étale cohomology, Lefschetz theorems and number of points of singular varieties over finite fields,, Mosc. Math. J., 2 (2002), 589.
|
[9] |
S. Ghorpade and G. Lachaud, Number of solutions of equations over finite fields and a conjecture of Lang and Weil,, in, (2002), 269.
|
[10] |
V. Guruswami and A. Vardy, Maximum-likelihood decoding of Reed-Solomon codes is NP-hard,, IEEE Trans. Inform. Theory, 51 (2005), 2249.
doi: 10.1109/TIT.2005.850102. |
[11] |
J. Heintz, Definability and fast quantifier elimination in algebraically closed fields,, Theoret. Comput. Sci., 24 (1983), 239.
doi: 10.1016/0304-3975(83)90002-6. |
[12] |
N. Katz, Sums of Betti numbers in arbitrary characteristic,, Finite Fields Appl., 7 (2001), 29.
doi: 10.1006/ffta.2000.0303. |
[13] |
E. Kunz, "Introduction to Commutative Algebra and Algebraic Geometry,'', Birkhäuser, (1985).
|
[14] |
A. Lascoux and P. Pragracz, Jacobian of symmetric polynomials,, Ann. Comb., 6 (2002), 169.
doi: 10.1007/PL00012583. |
[15] |
J. Li and D. Wan, On the subset sum problem over finite fields,, Finite Fields Appl., 14 (2008), 911.
doi: 10.1016/j.ffa.2008.05.003. |
[16] |
Y.-J. Li and D. Wan, On error distance of Reed-Solomon codes,, Sci. China Ser. A, 51 (2008), 1982.
doi: 10.1007/s11425-008-0066-3. |
[17] |
R. Lidl and H. Niederreiter, "Finite Fields,'' 2nd edition,, Addison-Wesley, (1997).
|
[18] |
F. Rodier, Borne sur le degré des polynômes presque parfaitement non-linéaires,, in, (2009), 169.
|
[19] |
I. R. Shafarevich, "Basic Algebraic Geometry: Varieties in projective space,'', Springer, (1994).
|
[20] |
D. Wan, Generators and irreducible polynomials over finite fields,, Math. Comp., 66 (1997), 1195.
doi: 10.1090/S0025-5718-97-00835-1. |
show all references
References:
[1] |
A. Adolphson and S. Sperber, On the degree of the L-function associated with an exponential sum,, Compos. Math., 68 (1988), 125.
|
[2] |
Y. Aubry and F. Rodier, Differentially 4-uniform functions,, in, (2010), 1.
|
[3] |
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.
doi: 10.1016/j.ffa.2005.03.003. |
[4] |
Q. Cheng and E. Murray, On deciding deep holes of Reed-Solomon codes,, in, (2007), 296.
doi: 10.1007/978-3-540-72504-6_27. |
[5] |
R. Coulter and M. Henderson, A note on the roots of trinomials over a finite field,, Bull. Austral. Math. Soc., 69 (2004), 429.
doi: 10.1017/S0004972700036200. |
[6] |
T. Ernst, Generalized Vandermonde determinants,, report 2000: 6 Matematiska Institutionen, (2000). Google Scholar |
[7] |
D. K. Faddeev and I. S. Sominskii, "Problems in Higher Algebra,", Freeman, (1965).
|
[8] |
S. Ghorpade and G. Lachaud, Étale cohomology, Lefschetz theorems and number of points of singular varieties over finite fields,, Mosc. Math. J., 2 (2002), 589.
|
[9] |
S. Ghorpade and G. Lachaud, Number of solutions of equations over finite fields and a conjecture of Lang and Weil,, in, (2002), 269.
|
[10] |
V. Guruswami and A. Vardy, Maximum-likelihood decoding of Reed-Solomon codes is NP-hard,, IEEE Trans. Inform. Theory, 51 (2005), 2249.
doi: 10.1109/TIT.2005.850102. |
[11] |
J. Heintz, Definability and fast quantifier elimination in algebraically closed fields,, Theoret. Comput. Sci., 24 (1983), 239.
doi: 10.1016/0304-3975(83)90002-6. |
[12] |
N. Katz, Sums of Betti numbers in arbitrary characteristic,, Finite Fields Appl., 7 (2001), 29.
doi: 10.1006/ffta.2000.0303. |
[13] |
E. Kunz, "Introduction to Commutative Algebra and Algebraic Geometry,'', Birkhäuser, (1985).
|
[14] |
A. Lascoux and P. Pragracz, Jacobian of symmetric polynomials,, Ann. Comb., 6 (2002), 169.
doi: 10.1007/PL00012583. |
[15] |
J. Li and D. Wan, On the subset sum problem over finite fields,, Finite Fields Appl., 14 (2008), 911.
doi: 10.1016/j.ffa.2008.05.003. |
[16] |
Y.-J. Li and D. Wan, On error distance of Reed-Solomon codes,, Sci. China Ser. A, 51 (2008), 1982.
doi: 10.1007/s11425-008-0066-3. |
[17] |
R. Lidl and H. Niederreiter, "Finite Fields,'' 2nd edition,, Addison-Wesley, (1997).
|
[18] |
F. Rodier, Borne sur le degré des polynômes presque parfaitement non-linéaires,, in, (2009), 169.
|
[19] |
I. R. Shafarevich, "Basic Algebraic Geometry: Varieties in projective space,'', Springer, (1994).
|
[20] |
D. Wan, Generators and irreducible polynomials over finite fields,, Math. Comp., 66 (1997), 1195.
doi: 10.1090/S0025-5718-97-00835-1. |
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