A new bound for the orthogonality defect of HKZ reduced lattices (Q6573195)
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scientific article; zbMATH DE number 7881683
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A new bound for the orthogonality defect of HKZ reduced lattices |
scientific article; zbMATH DE number 7881683 |
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A new bound for the orthogonality defect of HKZ reduced lattices (English)
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16 July 2024
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The process of going from a basis in which the vectors are long and non-orthogonal to a basis which is relatively short and has nearly orthogonal vectors is called lattice reduction. In this paper, it is the specific definitions of the Hermite-Korkin-Zolotarev (HMZ) lattice reduction that is used. The authors give a sharp upper bound on the orthogonality defect of HKZ reduced bases up to dimension \(3\) and use it to determine a general upper bound for the orthogonality defect of HKZ reduced bases of arbitrary rank which is sharper than existing bounds.
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lattices
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quadratic forms
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reduction theory
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geometry of numbers
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