ISSN:
1439-6912
Keywords:
11 H 06
;
11 H 50
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Letλ i(L), λi(L*) denote the successive minima of a latticeL and its reciprocal latticeL *, and let [b1,..., b n ] be a basis ofL that is reduced in the sense of Korkin and Zolotarev. We prove that and , where andγ j denotes Hermite's constant. As a consequence the inequalities are obtained forn≥7. Given a basisB of a latticeL in ℝ m of rankn andx∃ℝ m , we define polynomial time computable quantitiesλ(B) andΜ(x,B) that are lower bounds for λ1(L) andΜ(x,L), whereΜ(x,L) is the Euclidean distance fromx to the closest vector inL. If in additionB is reciprocal to a Korkin-Zolotarev basis ofL *, then λ1(L)≤γ n * λ(B) and .
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02128669
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