Construction of some unimodular lattices with long shadows

Masaaki Harada

doi:10.1142/S1793042111004794

Construction of some unimodular lattices with long shadows

Masaaki Harada

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

2 Citations (Scopus)

Abstract

In this paper, we construct odd unimodular lattices in dimensions n = 36,37 having minimum norm 3 and 4s = n-16, where s is the minimum norm of the shadow. We also construct odd unimodular lattices in dimensions n = 41,43,44 having minimum norm 4 and 4s = n-24.

Original language	English
Pages (from-to)	1345-1358
Number of pages	14
Journal	International Journal of Number Theory
Volume	7
Issue number	5
DOIs	https://doi.org/10.1142/S1793042111004794
Publication status	Published - 2011 Aug
Externally published	Yes

Keywords

Unimodular lattice
self-dual code
shadow

ASJC Scopus subject areas

Algebra and Number Theory

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10.1142/S1793042111004794

Cite this

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title = "Construction of some unimodular lattices with long shadows",

abstract = "In this paper, we construct odd unimodular lattices in dimensions n = 36,37 having minimum norm 3 and 4s = n-16, where s is the minimum norm of the shadow. We also construct odd unimodular lattices in dimensions n = 41,43,44 having minimum norm 4 and 4s = n-24.",

keywords = "Unimodular lattice, self-dual code, shadow",

author = "Masaaki Harada",

note = "Funding Information: The author would like to thank the anonymous referee for helpful suggestions that improved Proposition 3.2 and Corollary 4.2. This work was supported by JST PRESTO program.",

year = "2011",

month = aug,

doi = "10.1142/S1793042111004794",

language = "English",

volume = "7",

pages = "1345--1358",

journal = "International Journal of Number Theory",

issn = "1793-0421",

publisher = "World Scientific Publishing Co. Pte Ltd",

number = "5",

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T1 - Construction of some unimodular lattices with long shadows

AU - Harada, Masaaki

N1 - Funding Information: The author would like to thank the anonymous referee for helpful suggestions that improved Proposition 3.2 and Corollary 4.2. This work was supported by JST PRESTO program.

PY - 2011/8

Y1 - 2011/8

N2 - In this paper, we construct odd unimodular lattices in dimensions n = 36,37 having minimum norm 3 and 4s = n-16, where s is the minimum norm of the shadow. We also construct odd unimodular lattices in dimensions n = 41,43,44 having minimum norm 4 and 4s = n-24.

AB - In this paper, we construct odd unimodular lattices in dimensions n = 36,37 having minimum norm 3 and 4s = n-16, where s is the minimum norm of the shadow. We also construct odd unimodular lattices in dimensions n = 41,43,44 having minimum norm 4 and 4s = n-24.

KW - Unimodular lattice

KW - self-dual code

KW - shadow

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DO - 10.1142/S1793042111004794

M3 - Article

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EP - 1358

JO - International Journal of Number Theory

JF - International Journal of Number Theory

IS - 5

ER -

Construction of some unimodular lattices with long shadows

Abstract

Keywords

ASJC Scopus subject areas

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