Matches in SemOpenAlex for { <https://semopenalex.org/work/W2952985264> ?p ?o ?g. }
Showing items 1 to 87 of
87
with 100 items per page.
- W2952985264 abstract "In this paper we review the technique to solve the CVP based on dual HKZ-bases by J. Bloemer. The technique is based on the transference theorems given by Banaszczyk which imply some necessary conditions on the coefficients of the closest vectors with respect to a basis whose dual is HKZ reduced. Recursively, starting with the last coefficient, intervals of length i can be derived for the i-th coefficient of any closest vector. This leads to n! candidates for closest vectors. In this paper we refine the necessary conditions derived from the transference theorems, giving an exponential reduction of the number of candidates. The improvement is due to the fact that the lengths of the intervals are not independent. In the original algorithm the candidates for a coefficient pair (a_i,a_{i+1}) correspond to the integer points in a rectangle of volume i(i+1). In our analysis we show that the candidates for (a_i,a_{i+1}) in fact lie in an ellipse with transverse and conjugate diameter i+1, respectively i. This reduces the overall number of points to be enumerated by an exponential factor of about 0.886^n. We further show how a choice of the coefficients (a_n,...,a_{i+1}) influences the interval from which a_i can be chosen. Numerical computations show that these considerations allow to bound the number of points to be enumerated by n^{0.75 n} for 10 <= n <= 2000. Under the assumption that the Gaussian heuristic for the length of the shortest nonzero vector in a lattice is tight, this number can even be bounded by 2^{-2n} n^{n/2}." @default.
- W2952985264 created "2019-06-27" @default.
- W2952985264 creator A5028915374 @default.
- W2952985264 creator A5049125794 @default.
- W2952985264 date "2012-01-25" @default.
- W2952985264 modified "2023-09-27" @default.
- W2952985264 title "Improvements in closest point search based on dual HKZ-bases" @default.
- W2952985264 cites W1981142474 @default.
- W2952985264 cites W1997002146 @default.
- W2952985264 cites W2000956176 @default.
- W2952985264 cites W2001093624 @default.
- W2952985264 cites W2026129593 @default.
- W2952985264 cites W2140940105 @default.
- W2952985264 hasPublicationYear "2012" @default.
- W2952985264 type Work @default.
- W2952985264 sameAs 2952985264 @default.
- W2952985264 citedByCount "0" @default.
- W2952985264 crossrefType "posted-content" @default.
- W2952985264 hasAuthorship W2952985264A5028915374 @default.
- W2952985264 hasAuthorship W2952985264A5049125794 @default.
- W2952985264 hasConcept C114614502 @default.
- W2952985264 hasConcept C118615104 @default.
- W2952985264 hasConcept C121332964 @default.
- W2952985264 hasConcept C12426560 @default.
- W2952985264 hasConcept C126255220 @default.
- W2952985264 hasConcept C134306372 @default.
- W2952985264 hasConcept C151376022 @default.
- W2952985264 hasConcept C163716315 @default.
- W2952985264 hasConcept C173801870 @default.
- W2952985264 hasConcept C199360897 @default.
- W2952985264 hasConcept C2524010 @default.
- W2952985264 hasConcept C2778067643 @default.
- W2952985264 hasConcept C2781302577 @default.
- W2952985264 hasConcept C28719098 @default.
- W2952985264 hasConcept C28826006 @default.
- W2952985264 hasConcept C33923547 @default.
- W2952985264 hasConcept C41008148 @default.
- W2952985264 hasConcept C62520636 @default.
- W2952985264 hasConcept C74261601 @default.
- W2952985264 hasConcept C97137487 @default.
- W2952985264 hasConceptScore W2952985264C114614502 @default.
- W2952985264 hasConceptScore W2952985264C118615104 @default.
- W2952985264 hasConceptScore W2952985264C121332964 @default.
- W2952985264 hasConceptScore W2952985264C12426560 @default.
- W2952985264 hasConceptScore W2952985264C126255220 @default.
- W2952985264 hasConceptScore W2952985264C134306372 @default.
- W2952985264 hasConceptScore W2952985264C151376022 @default.
- W2952985264 hasConceptScore W2952985264C163716315 @default.
- W2952985264 hasConceptScore W2952985264C173801870 @default.
- W2952985264 hasConceptScore W2952985264C199360897 @default.
- W2952985264 hasConceptScore W2952985264C2524010 @default.
- W2952985264 hasConceptScore W2952985264C2778067643 @default.
- W2952985264 hasConceptScore W2952985264C2781302577 @default.
- W2952985264 hasConceptScore W2952985264C28719098 @default.
- W2952985264 hasConceptScore W2952985264C28826006 @default.
- W2952985264 hasConceptScore W2952985264C33923547 @default.
- W2952985264 hasConceptScore W2952985264C41008148 @default.
- W2952985264 hasConceptScore W2952985264C62520636 @default.
- W2952985264 hasConceptScore W2952985264C74261601 @default.
- W2952985264 hasConceptScore W2952985264C97137487 @default.
- W2952985264 hasLocation W29529852641 @default.
- W2952985264 hasOpenAccess W2952985264 @default.
- W2952985264 hasPrimaryLocation W29529852641 @default.
- W2952985264 hasRelatedWork W1525388079 @default.
- W2952985264 hasRelatedWork W1596035709 @default.
- W2952985264 hasRelatedWork W168334256 @default.
- W2952985264 hasRelatedWork W1901474581 @default.
- W2952985264 hasRelatedWork W1973240108 @default.
- W2952985264 hasRelatedWork W2003397294 @default.
- W2952985264 hasRelatedWork W2067522133 @default.
- W2952985264 hasRelatedWork W2093295255 @default.
- W2952985264 hasRelatedWork W2258956566 @default.
- W2952985264 hasRelatedWork W2889735464 @default.
- W2952985264 hasRelatedWork W2897820666 @default.
- W2952985264 hasRelatedWork W2902613999 @default.
- W2952985264 hasRelatedWork W2952134317 @default.
- W2952985264 hasRelatedWork W2952676036 @default.
- W2952985264 hasRelatedWork W2952875504 @default.
- W2952985264 hasRelatedWork W2963825179 @default.
- W2952985264 hasRelatedWork W3169533302 @default.
- W2952985264 hasRelatedWork W3185152180 @default.
- W2952985264 hasRelatedWork W774445692 @default.
- W2952985264 hasRelatedWork W1833837630 @default.
- W2952985264 isParatext "false" @default.
- W2952985264 isRetracted "false" @default.
- W2952985264 magId "2952985264" @default.
- W2952985264 workType "article" @default.