J. L. Alfonsín, On variations of the subset sum problem, Discrete Applied Mathematics, vol.81, issue.1-3, pp.1-7, 1998.
DOI : 10.1016/S0166-218X(96)00105-9

J. L. Alfonsín, The Diophantine Frobenius Problem, Oxford Lecture Series in Mathematics and Its Applications, 2005.

M. Bardet, Étude des systèmes algébriques surdéterminés. applications aux codes correcteurs et à la cryptographie, 2004.

M. Bardet, J. Faugère, and B. Salvy, On the Complexity of the F5 Gröbner basis Algorithm, Journal of Symbolic Computation, pp.1-24, 2014.

M. Bardet, J. Faugère, B. Salvy, and B. Yang, Asymptotic behaviour of the degree of regularity of semi-regular polynomial systems, MEGA'05, 2005. Eighth International Symposium on Effective Methods in Algebraic Geometry, 2005.

T. Becker and V. Weispfenning, of Graduate Texts in Mathematics computational approach to commutative algebra, In cooperation with Heinz Kredel. URL http, Gröbner bases, vol.141, pp.978-979, 1993.

W. Bosma, J. Cannon, and C. Playoust, The Magma Algebra System I: The User Language, Journal of Symbolic Computation, vol.24, issue.3-4, pp.235-265, 1993.
DOI : 10.1006/jsco.1996.0125

B. Buchberger, A theoretical basis for the reduction of polynomials to canonical forms, ACM SIGSAM Bulletin, vol.10, issue.3, pp.19-29, 1976.
DOI : 10.1145/1088216.1088219

M. Caboara, G. De-dominicis, and L. Robbiano, Multigraded Hilbert functions and Buchberger algorithm, Proceedings of the 1996 international symposium on Symbolic and algebraic computation , ISSAC '96, pp.72-78, 1996.
DOI : 10.1145/236869.236901

S. Collart, M. Kalkbrenner, and D. Mall, Converting bases with the Gröbner walk, Journal of Symbolic Computation, vol.24, pp.3-4, 1997.

G. Dalzotto and E. Sbarra, Computations in weighted polynomial rings, Analele Stiintifice ale Universitatii Ovidius Constanta, vol.14, issue.2, pp.31-44, 2006.

M. Pellikaan and R. , Gröbner bases for codes. No. 4 in Algorithms and Computation in Mathematics, pp.237-259, 1999.

W. Decker, G. Greuel, G. Pfister, and H. Schönemann, Singular 3-1-6 ? A computer algebra system for polynomial computations, 2012.

A. Dickenstein and I. Z. Emiris, Solving Polynomial Equations: Foundations, Algorithms , and Applications, 2010.

D. Eisenbud, Commutative algebra of Graduate Texts in Mathematics, pp.978-979, 1995.

J. Faugère, A new efficient algorithm for computing Gröbner bases (F 4 ), algebraic geometry, pp.61-88, 1998.

J. Faugère, A new efficient algorithm for computing Gröbner bases without reduction to zero (F 5 ), Proceedings of the 2002 International Symposium on Symbolic and Algebraic Computation, pp.75-83, 2002.

J. Faugère, P. Gianni, D. Lazard, and T. Mora, Efficient Computation of Zero-dimensional Gr??bner Bases by Change of Ordering, Journal of Symbolic Computation, vol.16, issue.4, pp.329-344, 1993.
DOI : 10.1006/jsco.1993.1051

J. Faugère, M. Safey-el-din, and T. Verron, On the complexity of computing Gröbner bases for quasi-homogeneous systems, Proceedings of the 2013 International Symposium on Symbolic and Algebraic Computation. ISSAC '13, 2013.

J. Faugère, FGb: A Library for Computing Gr??bner Bases, Mathematical Software -ICMS 2010, 2010.
DOI : 10.1007/978-3-642-15582-6_17

J. Faugère, P. Gaudry, L. Huot, and G. Renault, Using Symmetries in the Index Calculus for Elliptic Curves Discrete Logarithm, Journal of Cryptology, vol.32, issue.1, pp.1-41, 2013.
DOI : 10.1007/s00145-013-9158-5

R. Fröberg, An inequality for Hilbert series of graded algebras., MATHEMATICA SCANDINAVICA, vol.56, pp.117-144, 1985.
DOI : 10.7146/math.scand.a-12092

P. Gaudry, Index calculus for abelian varieties of small dimension and the elliptic curve discrete logarithm problem, gröbner Bases in Cryptography, Coding Theory, and Algebraic Combinatorics. URL http, pp.1690-1702, 2009.
DOI : 10.1016/j.jsc.2008.08.005

URL : https://hal.archives-ouvertes.fr/inria-00337631

D. R. Grayson and M. E. Stillman, Macaulay2, a software system for research in algebraic geometry, 2014.

E. Guerrini, A. Rimoldi, M. Sala, S. Sakata, T. Mora et al., FGLM-Like Decoding: from Fitzpatrick???s Approach to Recent Developments, Gröbner Bases, Coding, and Cryptography, pp.197-218978, 2009.
DOI : 10.1007/978-3-540-93806-4_12

D. A. Leonard, A weighted module view of integral closures of affine domains of type I, Advances in Mathematics of Communications, vol.3, issue.1, pp.1-11, 2009.
DOI : 10.3934/amc.2009.3.1

J. S. Milne, Algebraic geometry (v5.22) Available at www.jmilne.org/math, 2012.

G. Moreno-socías, Autour de la fonction de Hilbert-Samuel (escaliers d'idéaux polynomiaux), p.151245, 1991.

G. Moreno-socías, Revlex standard bases of generic complete intersections, 1996.

G. Moreno-socías, Degrevlex Gr??bner bases of generic complete intersections, Journal of Pure and Applied Algebra, vol.180, issue.3, pp.263-283, 2003.
DOI : 10.1016/S0022-4049(02)00297-9

I. M. Niven, H. S. Zuckerman, and H. L. Montgomery, An introduction to the theory of numbers, 1991.

K. Pardue, Generic sequences of polynomials, Journal of Algebra, vol.324, issue.4, pp.579-590, 2010.
DOI : 10.1016/j.jalgebra.2010.04.018

L. Reid, L. G. Roberts, and M. Roitman, On complete intersections and their Hilbert functions, Bulletin canadien de math??matiques, vol.34, issue.4, pp.525-535, 1991.
DOI : 10.4153/CMB-1991-083-9

B. Sturmfels, Algorithms in Invariant Theory (Texts and Monographs in Symbolic Computation, 2008.

C. Traverso, Hilbert Functions and the Buchberger Algorithm, Journal of Symbolic Computation, vol.22, issue.4, pp.355-376, 1996.
DOI : 10.1006/jsco.1996.0056