On distances in lattices from algebraic number fields

Artūras Dubickas; Min Sha; Igor E. Shparlinski

doi:10.17323/1609-4514-2017-17-2-239-268

On distances in lattices from algebraic number fields

Artūras Dubickas, Min Sha, Igor E. Shparlinski

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

In this paper, we study a classical construction of lattices from number fields and obtain a series of new results about their minimum distance and other characteristics by introducing a new measure of algebraic numbers. In particular, we show that when the number fields have few complex embeddings, the minimum distances of these lattices can be computed exactly.

Original language	English
Pages (from-to)	239-268
Number of pages	30
Journal	Moscow Mathematical Journal
Volume	17
Issue number	2
DOIs	https://doi.org/10.17323/1609-4514-2017-17-2-239-268
Publication status	Published - 2017
Externally published	Yes

Keywords

lattice
minimum distance
algebraic number field
Pisot numbers
multinacci number
algebraic unit

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10.17323/1609-4514-2017-17-2-239-268

Cite this

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title = "On distances in lattices from algebraic number fields",

abstract = "In this paper, we study a classical construction of lattices from number fields and obtain a series of new results about their minimum distance and other characteristics by introducing a new measure of algebraic numbers. In particular, we show that when the number fields have few complex embeddings, the minimum distances of these lattices can be computed exactly.",

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author = "Artūras Dubickas and Min Sha and Shparlinski, \{Igor E.\}",

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AU - Dubickas, Artūras

AU - Sha, Min

AU - Shparlinski, Igor E.

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AB - In this paper, we study a classical construction of lattices from number fields and obtain a series of new results about their minimum distance and other characteristics by introducing a new measure of algebraic numbers. In particular, we show that when the number fields have few complex embeddings, the minimum distances of these lattices can be computed exactly.

KW - lattice

KW - minimum distance

KW - algebraic number field

KW - Pisot numbers

KW - multinacci number

KW - algebraic unit

UR - https://www.scopus.com/pages/publications/85021745648

U2 - 10.17323/1609-4514-2017-17-2-239-268

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SP - 239

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JO - Moscow Mathematical Journal

JF - Moscow Mathematical Journal

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On distances in lattices from algebraic number fields

Abstract

Keywords

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