K. Belabas, A relative van Hoeij algorithm over number fields, J. Symb. Comput, vol.37, issue.5, pp.641-668, 2004.

K. Belabas, Topics in computational algebraic number theory, J. Théor. Nr. Bordx, vol.16, issue.1, pp.19-63, 2004.

D. Boneh, Finding smooth integers in short intervals using CRT decoding, J. Comput. Syst. Sci, vol.64, issue.4, pp.768-784, 2002.

H. Cohen, A course in computational algebraic number theory, Graduate Texts in Math, vol.138, 1993.

H. Cohen, Advanced topics in computational number theory, Graduate Texts in Math, vol.193, 2000.

H. Cohn and N. Heninger, Ideal forms of Coppersmith's theorem and Guruswami-Sudan list decoding, 2010.

J. G. Dumas, C. Pernet, and Z. Wan, Efficient computation of the characteristic polynomial, ISSAC'05: Proceedings of the 2005 international symposium on symbolic and algebraic computation, pp.140-147, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00004056

H. M. Edwards, Galois theory, Graduate Texts in Math, vol.101, 1984.

G. D. Forney, Generalized minimum distance decoding, IEEE Trans. Inform. Theory IT, vol.12, issue.2, pp.125-131, 1966.

I. Gohberg, P. Lancaster, and L. Rodman, Matrix polynomials, 1982.

O. Goldreich, D. Ron, and M. Sudan, Chinese remaindering with errors, IEEE Trans. Inform. Theory, vol.46, issue.4, pp.1330-1338, 2000.

V. Guruswami, Constructions of codes from number fields, IEEE Trans. Inform. Theory, vol.49, issue.3, pp.594-603, 2003.

V. Guruswami, List decoding of error-correcting codes, Lecture Notes in Comput. Sci, vol.3282, 2004.

V. Guruswami, A. Sahai, and M. Sudan, Soft-decision" decoding of Chinese remainder codes, Proceedings of the 41st Annual Symposium on Foundations of Computer Science, pp.159-168, 2000.

V. Guruswami and M. Sudan, Improved decoding of Reed-Solomon and algebraic-geometry codes, IEEE Trans. Inform. Theory, vol.45, issue.6, pp.1757-1767, 1999.

V. Guruswami and M. Sudan, Extensions to the Johnson bound, 2001.

G. Hanrot, X. Pujol, and D. Stehlé, Algorithms for the shortest and closest lattice vector problems, Coding and cryptology, vol.6639, pp.159-190, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00640637

E. Horowitz and S. Sahni, On computing the exact determinant of matrices with polynomial entries, J. Assoc. Comput. Mach, vol.22, pp.38-50, 1975.

N. Howgrave-graham, Finding small roots of univariate modular equations revisit, Cryptography and Coding, vol.1355, pp.131-142, 1997.

S. M. Johnson, A new upper bound for error-correcting codes, IRE Trans. IT, vol.8, issue.3, pp.203-207, 1962.

S. M. Johnson, Improved asymptotic bounds for error-correcting codes, IEEE Trans. Inform. Theory IT, vol.9, issue.3, pp.198-205, 1963.

B. Just, Mathematical Foundations of Computer Science, Lecture Notes in Comput. Sci, vol.379, pp.314-320, 1989.

B. Just, Integer relations among algebraic numbers, Math. Comp, vol.54, issue.189, pp.467-477, 1990.

L. Kronecker, Grundzüge einer arithmetischen Theorie der algebraischen Grössen, J. Reine. Angew. Math, vol.92, pp.1-122, 1882.

S. Landau, Factoring polynomials over algebraic number fields, SIAM J. Comput, vol.14, issue.1, pp.184-195, 1985.

A. K. Lenstra, Factoring polynomials over algebraic number fields, Computer algebra, vol.162, pp.245-254, 1983.

A. K. Lenstra, H. W. Lenstra, and L. Lovász, Factoring polynomials with rational coefficients, Math. Ann, vol.261, issue.4, pp.515-534, 1982.

H. W. Lenstra, J. K. Lenstra, and L. G. Meertens, Mathematics and computer science II, Fundamental contributions in the Netherlands since 1945, Codes from algebraic number fields. Hazewinkel, vol.4, pp.95-104, 1986.

H. W. Lenstra, Algorithms in algebraic number theory, Bull. Amer. Math. Soc, vol.26, issue.2, pp.211-244, 1992.

D. M. Mandelbaum, On a class of arithmetic codes and a decoding algorithm, IEEE Trans. Inform. Theory IT, vol.22, issue.1, pp.85-88, 1976.

D. A. Marcus, Number fields, 1977.

M. T. Mcclellan, The exact solution of systems of linear equations with polynomial coefficients, J. Assoc. Comput. Mach, vol.20, pp.563-588, 1973.

M. Mignotte, An inequality about factors of polynomials, Math. Comp, vol.28, pp.1153-1157, 1974.

W. Narkiewicz, Elementary and analytic theory of algebraic numbers, 2004.

P. Q. Nguyen and D. Stehlé, Floating-point LLL revisited, Lecture Notes in Comput. Sci, vol.3494, pp.215-233, 2005.
URL : https://hal.archives-ouvertes.fr/inria-00000377

P. Q. Nguyen and D. Stehlé, An LLL algorithm with quadratic complexity, SIAM J. Comput, vol.39, issue.3, pp.874-903, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00550981

V. Pan, Sequential and parallel complexity of approximate evaluation of polynomial zeros, Comput. Math. Appl, vol.14, issue.8, pp.591-622, 1987.

H. Richter, Bemerkung zur Norm der Inversen einer Matrix, Arch. Math, vol.5, pp.447-448, 1954.

V. Sidorenko, G. Schmidt, E. Gabidulin, M. Bossert, and V. Afanassiev, On polyalphabetic block codes, Proc. IEEE ISOC Information Theory Workshop 2005 on Coding and Complexity, pp.207-210, 2005.

J. Stoer and R. Bulirsch, Introduction to numerical analysis, Texts in Appl. Math, vol.12, 1993.

A. Storjohann, Algorithms for matrix canonical forms, 2000.

M. Sudan, Decoding of Reed-Solomon codes beyond the error-correction bound, J. Complex, vol.13, issue.1, pp.180-193, 1997.

M. Sudan, Ideal error-correcting codes: Unifying algebraic and number-theoretic algorithms, Proc. Int. 14th Symp, vol.2227, pp.36-45, 2001.