Constructions of Orthonormal Lattices and Quaternion Division Algebras for Totally Real Number Fields

Sethuraman, B. A.; Oggier, Frédérique

doi:10.1007/978-3-540-77224-8_18

Cited by 6 publications

(5 citation statements)

References 11 publications

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“…Codewords are usually built over the complex field. However for ultra wideband communication, one needs to design them over the real field [12]. Thus, having the construction of rotated lattices as our goal, we are interested in constructing dense lattices from octonion orders over a totally real number field.…”

Section: Introductionmentioning

confidence: 99%

Lattices Associated with Octonion Algebras

Brasil¹,

Benedito

Costa³

2018

JCIS

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Abstract-In this paper we propose a construction of lattices in dimension 8n via octonion orders over a totally real number field. To show the potential of this construction, we present rotated versions of E 8 , Λ 16 , the densest known lattices in these dimensions and a lattice with the same density of the Barnes-Wall lattice in dimension 32. Perspectives applications of these lattices based on octonion algebras are in lattice based cryptography and lattice coding for MIMO and MISO channels.

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Section: Introductionmentioning

confidence: 99%

Lattices Associated with Octonion Algebras

Brasil¹,

Benedito

Costa³

2018

JCIS

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“…Este trabalho foi parcialmente financiado pelo CNPq 312926/2013-8 e CAPES. reticulados ideais [13] ou reticulados do tipo traço [18], os quais são obtidos por uma construção traço escalonada.…”

Section: Introductionunclassified

Reticulados associados a álgebra dos octônios

Nelson¹,

Benedito²,

Costa³

2017

Anais De XXXV Simpósio Brasileiro De Telecomunicações E Processamento De Sinais

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“…Codewords are usually (in narrow band systems) built over the complex field. However for ultra wideband communication, one needs to design them over the real field [18]. Thus, having the construction of rotated lattices as our goal, we are interested in constructing dense lattices from maximal orders of the division algebras over a totally real number field.…”

Section: Introductionmentioning

confidence: 99%

Lattices from maximal quaternion orders over totally real number fields

Benedito¹,

Alves²,

Costa³

2015

Anais De XXXIII Simpósio Brasileiro De Telecomunicações

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In this paper we propose a framework to construct space-time codes over lattices in dimensions 4n via ideals from maximal orders of a quaternion algebra whose center is a totally real number field. For n = 1 and n = 2 it was possible to construct rotated versions of the densest lattices in their dimensions, D4 and E8. These constructions provide explicit forms for the generator matrix and other algebraic invariants allowing to analyze meaningful performance parameters for coding such as density, diversity and minimal product distance.

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Constructions of Orthonormal Lattices and Quaternion Division Algebras for Totally Real Number Fields

Cited by 6 publications

References 11 publications

Lattices Associated with Octonion Algebras

Lattices Associated with Octonion Algebras

Reticulados associados a álgebra dos octônios

Lattices from maximal quaternion orders over totally real number fields

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