Reducing lattice bases by means of approximations

@inproceedings{Buchmann1994ReducingLB,
  title={Reducing lattice bases by means of approximations},
  author={Johannes A. Buchmann},
  booktitle={ANTS},
  year={1994}
}
Let L be a k-dimensional lattice in IR m with basis B = (b 1 ; : : : ; b k). Let A = (a1; : : : ; ak) be a rational approximation to B. Assume that A has rank k and a lattice basis reduction algorithm applied to the columns of A yields a transformation T = (t 1 ; : : : ; t k) 2 GL(k; Z Z) such that At i sii(L(A)) where L(A) is the lattice generated by the columns of A, i(L(A)) is the i-th successive minimum of that lattice and si 1, 1 i k. For c > 0 we determine which precision of A is… CONTINUE READING

References

Publications referenced by this paper.
Showing 1-10 of 10 references

Computing a reduced lattice basis from a generating system, preprint

  • J Buke, V Buchmann, Kessler
  • Computing a reduced lattice basis from a…
  • 1993

Korkine-Zolotarev bases and successive minima of a lattice and its dual lattice

  • J C Lalesch, H W Lagarias, C P Lenstra Jr, Schnorr
  • Combinatorica
  • 1990

Schrijver: Geometric algorithms and combinatorial optimization

  • M Grloschri, L Grr Otschel, A Lovv Asz
  • Schrijver: Geometric algorithms and combinatorial…
  • 1988

Pohst: A modiication of the LLL Reduction Algorithm

  • M Po
  • J. Symbolic Computation
  • 1987

Lovv asz: Factoring polynomials with rational coeecients

  • A K Lelelo, H W Lenstra, L Lenstra Jr
  • Math. Ann
  • 1982

Birkhh auser

  • B L Wagr, H Van Der Waerden, Gross
  • Birkhh auser
  • 1968

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