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

• Main Author: Ferrari, Agnaldo J. [UNESP]
• Publication Date: 2024
• Other Authors: de Andrade, Antonio A. [UNESP], Interlando, José C., Alves, Carina [UNESP]
• Format: Article
• Language: eng
• Source: Repositório Institucional da UNESP
• Download full: http://dx.doi.org/10.13069/jacodesmath.v11i2.207; https://hdl.handle.net/11449/308167
• topic: Algebraic lattices; Cyclotomic fields; Minimum product distance; Signal 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(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.