Published June 16, 2025 | Version v1
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A Way of Constructing Lattice Packings of Equal Spheres Corresponding to the Packing Density of the Lambda Series

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The creation of cryptographic systems based on lattice theory is a promising line in the field of post-quantum cryptography. The aim of this work was to obtain new properties of lattices through related objects: dense packings of equal spheres. We propose a way of constructing lattice packings of equal spheres corresponding to the packing density of the Lambda series in dimensions 1–24, using a series of coefficients to the height of the fundamental parallelepiped of dimension (n−1): 1/2, 1/3, 1/2, 0, 1/2, 1/3, 1/2, −1, 1/2, 1/3, 1/2, 0, 1/2, 1/3, 1/2, −1, 1/2, 1/3, 1/2, 0, 1/2, 1/3, 1/2. The construction of lattice packings of equal spheres using this procedure was used up to dimension 11 inclusive.

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Dates

Accepted
2024-12-23

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