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pro vyhledávání: '"Unimodular lattices"'
Self-dual codes have been studied actively because they are connected with mathematical structures including block designs and lattices and have practical applications in quantum error-correcting codes and secret sharing schemes. Nevertheless, there
Externí odkaz:
http://arxiv.org/abs/2409.00404
Autor:
Bollauf, Maiara F., Lin, Hsuan-Yin
The theta series of a lattice has been extensively studied in the literature and is closely related to a critical quantity widely used in the fields of physical layer security and cryptography, known as the flatness factor, or equivalently, the smoot
Externí odkaz:
http://arxiv.org/abs/2403.16932
Autor:
Takada, Yuta
E. Bayer-Fluckiger gave a necessary and sufficient condition for a polynomial to be realized as the characteristic polynomial of a semisimple isometry of an even unimodular lattice, by describing the local-global obstruction, and the author extended
Externí odkaz:
http://arxiv.org/abs/2401.12620
Recently, a design criterion depending on a lattice's volume and theta series, called the secrecy gain, was proposed to quantify the secrecy-goodness of the applied lattice code for the Gaussian wiretap channel. To address the secrecy gain of Constru
Externí odkaz:
http://arxiv.org/abs/2303.08083
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Autor:
Xing, Hao
In this article, we study the relation between lattice basis and successive minima and give an estimate for the measure-theoretical distribution of successive minima. As consequences, we also discuss some logarithm laws associated to higher sucessive
Externí odkaz:
http://arxiv.org/abs/2212.14373
Autor:
Fregoli, Reynold, Zheng, Cheng
In this paper, we study the shrinking-target problem with target at infinity induced by the injectivity radius function under the action of a regular diagonalizable flow on $\operatorname{SL}_3(\mathbb R)/\operatorname{SL}_3(\mathbb Z)$. In particula
Externí odkaz:
http://arxiv.org/abs/2210.12508
Autor:
Harada, Masaaki
New $s$-extremal extremal unimodular lattices in dimensions $38$, $40$, $42$ and $44$ are constructed from self-dual codes over $\mathbb{F}_5$ by Construction A. In the process of constructing these codes, we obtain a self-dual $[44,22,14]$ code over
Externí odkaz:
http://arxiv.org/abs/2208.03617
Akademický článek
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