Well-rounded lattices from odd prime degree number fields in the ramified case
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Jefferson Luiz Rocha Bastos
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Trajano Pires da Nóbrega Neto
Abstract
Recently, algebraic lattices have been widely considered for applications in coding theory and cryptography. Likewise, well-rounded lattices have proven useful for signal transmission in MIMO and SISO wiretap channels. Previous works have conducted extensive studies on well-rounded algebraic lattices. One of them demonstrates the existence of well-rounded lattices obtained through the Minkowski embedding, representing the image of ℤ-modules in the ring of integers of cyclic number fields 𝕂 of odd prime degree p, where p remains unramified in the extension 𝕂/ℚ. In this work, we consider the case where p is ramified in 𝕂/ℚ and introduce a family of ℤ-modules that realize well-rounded algebraic lattices in ℝp for many (potentially infinitely many) values of p.
Funding statement: This work was partially supported by CNPq under Grant No. 405842/2023-6 and by CAPES-PRINT-UNESP.
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Communicated by: M. Henk
References
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Articles in the same Issue
- Frontmatter
- Combinatorics of stratified hyperbolic slices
- Godbersen’s conjecture for locally anti-blocking bodies
- A Hilbert metric for bounded symmetric domains
- On the generalized Suzuki curve
- The partition of PG(2, q3) arising from an order 3 planar collineation
- Well-rounded lattices from odd prime degree number fields in the ramified case
- Split Cayley hexagons via subalgebras of octonion algebras
- Relative Lipschitz saturation of complex algebraic varieties
- The prime grid contains arbitrarily large empty polygons
- The geometry of locally bounded rational functions
Articles in the same Issue
- Frontmatter
- Combinatorics of stratified hyperbolic slices
- Godbersen’s conjecture for locally anti-blocking bodies
- A Hilbert metric for bounded symmetric domains
- On the generalized Suzuki curve
- The partition of PG(2, q3) arising from an order 3 planar collineation
- Well-rounded lattices from odd prime degree number fields in the ramified case
- Split Cayley hexagons via subalgebras of octonion algebras
- Relative Lipschitz saturation of complex algebraic varieties
- The prime grid contains arbitrarily large empty polygons
- The geometry of locally bounded rational functions
