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pro vyhledávání: '"Well rounded lattices"'
Akademický článek
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It is well-known that the densest lattice sphere packings also typically have large kissing numbers. The sphere packing density maximization problem is known to have a solution among well-rounded lattices, of which the integer lattice $\mathbb{Z}^n$
Externí odkaz:
http://arxiv.org/abs/2107.00958
Autor:
Fukshansky, Lenny, Kogan, David
Publikováno v:
Moscow J. Comb. Number Th. 11 (2022) 79-96
We focus on two important classes of lattices, the well-rounded and the cyclic. We show that every well-rounded lattice in the plane is similar to a cyclic lattice, and use this cyclic parameterization to count planar well-rounded similarity classes
Externí odkaz:
http://arxiv.org/abs/2110.04905
Well-rounded lattices have been a topic of recent studies with applications in wiretap channels and in cryptography. A lattice of full rank in Euclidean space is called well-rounded if its set of minimal vectors spans the whole space. In this paper,
Externí odkaz:
http://arxiv.org/abs/1904.03510
Akademický článek
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Autor:
Damir, Mohamed Taoufiq, Karrila, Alex, Amorós, Laia, Gnilke, Oliver, Karpuk, David, Hollanti, Camilla
The design of lattice coset codes for wiretap channels is considered. Bounds on the eavesdropper's correct decoding probability and information leakage are first revisited. From these bounds, it is explicit that both the information leakage and error
Externí odkaz:
http://arxiv.org/abs/1609.07723
Autor:
Gnilke, Oliver W., Barreal, Amaro, Karrila, Alex, Tran, Ha Thanh Nguyen, Karpuk, David A., Hollanti, Camilla
The concept of well-rounded lattices has recently found important applications in the setting of a fading single-input single-output (SISO) wiretap channel. It has been shown that, under this setup, the property of being well-rounded is critical for
Externí odkaz:
http://arxiv.org/abs/1609.07666
For many wiretap channel models asymptotically optimal coding schemes are known, but less effort has been put into actual realizations of wiretap codes for practical parameters. Bounds on the mutual information and error probability when using coset
Externí odkaz:
http://arxiv.org/abs/1605.00419
Akademický článek
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Curt McMullen showed that every compact orbit for the action of the diagonal group on the space of lattices contains a well-rounded lattice. We extend this to all closed orbits.
Comment: 15 pages. This paper was originally a chapter in http://ar
Comment: 15 pages. This paper was originally a chapter in http://ar
Externí odkaz:
http://arxiv.org/abs/1405.5682