Nonsingular hypercubes and nonintersecting hyperboloids
- Author
- Kris Coolsaet (UGent)
- Organization
- Abstract
- Some ten years ago we managed to take a first step in the classification of nonsingular 2x2x2x2 hypercubes over a finite field by resolving the special case where the hypercubes can be written as a product of two 2x2x2 hypercubes, i.e., nonsingular 2x2x2x2 hypercubes of 12-rank two. We have now been able to extend this classification to hypercubes of 12-rank three, based on the connection between nonsingular hypercubes and bundles of nonintersecting quadrics in 3 dimensions. A bit surprisingly, the number of inequivalent non-singular hypercubes of 12-rank three is only of the same order of magnitude as in the case of 12-rank two. We also made some headway into the remaining case of 12-rank four. In particular, we prove that there are essentially only 2 nonsingular 2x2x2x2 hypercubes that correspond to a hyperbolic fibration of 3-dimensional projective space.
- Keywords
- Nonsingular hypercube, Classification, Bundle of quadrics, Hyperbolic fibration
Downloads
-
hypercubesrank3.pdf
- full text (Accepted manuscript)
- |
- open access
- |
- |
- 279.30 KB
-
(...).pdf
- full text (Published version)
- |
- UGent only
- |
- |
- 358.32 KB
Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-01HM8PHAM1FF1NYQHS5HDRCE0R
- MLA
- Coolsaet, Kris. “Nonsingular Hypercubes and Nonintersecting Hyperboloids.” DESIGNS CODES AND CRYPTOGRAPHY, vol. 92, 2023, pp. 93–112, doi:10.1007/s10623-023-01297-3.
- APA
- Coolsaet, K. (2023). Nonsingular hypercubes and nonintersecting hyperboloids. DESIGNS CODES AND CRYPTOGRAPHY, 92, 93–112. https://doi.org/10.1007/s10623-023-01297-3
- Chicago author-date
- Coolsaet, Kris. 2023. “Nonsingular Hypercubes and Nonintersecting Hyperboloids.” DESIGNS CODES AND CRYPTOGRAPHY 92: 93–112. https://doi.org/10.1007/s10623-023-01297-3.
- Chicago author-date (all authors)
- Coolsaet, Kris. 2023. “Nonsingular Hypercubes and Nonintersecting Hyperboloids.” DESIGNS CODES AND CRYPTOGRAPHY 92: 93–112. doi:10.1007/s10623-023-01297-3.
- Vancouver
- 1.Coolsaet K. Nonsingular hypercubes and nonintersecting hyperboloids. DESIGNS CODES AND CRYPTOGRAPHY. 2023;92:93–112.
- IEEE
- [1]K. Coolsaet, “Nonsingular hypercubes and nonintersecting hyperboloids,” DESIGNS CODES AND CRYPTOGRAPHY, vol. 92, pp. 93–112, 2023.
@article{01HM8PHAM1FF1NYQHS5HDRCE0R,
abstract = {{Some ten years ago we managed to take a first step in the classification of nonsingular 2x2x2x2 hypercubes over a finite field by resolving the special case where the hypercubes can be written as a product of two 2x2x2 hypercubes, i.e., nonsingular 2x2x2x2 hypercubes of 12-rank two. We have now been able to extend this classification to hypercubes of 12-rank three, based on the connection between nonsingular hypercubes and bundles of nonintersecting quadrics in 3 dimensions. A bit surprisingly, the number of inequivalent non-singular hypercubes of 12-rank three is only of the same order of magnitude as in the case of 12-rank two. We also made some headway into the remaining case of 12-rank four. In particular, we prove that there are essentially only 2 nonsingular 2x2x2x2 hypercubes that correspond to a hyperbolic fibration of 3-dimensional projective space.}},
author = {{Coolsaet, Kris}},
issn = {{0925-1022}},
journal = {{DESIGNS CODES AND CRYPTOGRAPHY}},
keywords = {{Nonsingular hypercube,Classification,Bundle of quadrics,Hyperbolic fibration}},
language = {{eng}},
pages = {{93--112}},
title = {{Nonsingular hypercubes and nonintersecting hyperboloids}},
url = {{http://doi.org/10.1007/s10623-023-01297-3}},
volume = {{92}},
year = {{2023}},
}
- Altmetric
- View in Altmetric
- Web of Science
- Times cited: