Characterization of totally real subfields of 2-power cyclotomic fields and applications to signal set design

A classification of all totally real subfields K of cyclotomic fields Q(ξ2r), for any r ≥ 4, and the fully-diverse related versions of the Zn-lattice are presented along with closed-form expressions for their minimum product distance. Any totally real subfield K of Q(ξ2r) must be of the form K = Q(ξ...

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Detalhes bibliográficos
Autores: Ferrari, Agnaldo J. [UNESP], de Andrade, Antonio A. [UNESP], Interlando, José C., Alves, Carina [UNESP]
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2024
País:Brasil
Recursos:Universidade Estadual Paulista (UNESP)
Repositorio:Repositório Institucional da UNESP
Idioma:inglés
OAI Identifier:oai:repositorio.unesp.br:11449/308167
Acesso em linha:http://dx.doi.org/10.13069/jacodesmath.v11i2.207
https://hdl.handle.net/11449/308167
Access Level:acceso abierto
Palavra-chave:Algebraic lattices
Cyclotomic fields
Minimum product distance
Signal design
Descrição
Resumo:A classification of all totally real subfields K of cyclotomic fields Q(ξ2r), for any r ≥ 4, and the fully-diverse related versions of the Zn-lattice are presented along with closed-form expressions for their minimum product distance. Any totally real subfield K of Q(ξ2r) must be of the form K = Q(ξ2s +ξ−1 2s), where s = r−j for some 0 ≤ j ≤ r−3. Signal constellations for transmitting information over both Gaussian and Rayleigh fading channels (which can be useful for mobile communications) can be carved out of those lattices.