On the coordinates of minimal vectors in a Minkowski-reduced basis

Ákos G. Horváth

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arXiv · 2102.05154

On the coordinates of minimal vectors in a Minkowski-reduced basis

Ákos G. Horváth

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Abstract

Finding the shortest vectors in a lattice is an NP-hard problem, so low-dimensional results also play an essential role in lattice reduction theory. Using Ryskov's result for the admissible centerings and Tammela's result for determining the Minkowski-reduced form, we prove that the absolute values of the coordinates of a minimal vector on a six-dimensional Minkowski-reduced basis are less than or equal to three. To sharpen P. Tammela's work, we combine some lattice geometry arguments with the aforementioned theoretical results.

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Ákos G. Horváth. 2021-02-09. On the coordinates of minimal vectors in a Minkowski-reduced basis. https://arxiv.org/abs/2102.05154

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