Trace forms of certain subfields of cyclotomic fields and applications

Yıl 2020, Cilt: 7 Sayı: 2, 141 - 160, 07.05.2020

Agnaldo José Ferrarı Antonio Aparecıdo De Andrade Robson Rıcardo De Araujo José Carmelo Interlando

https://doi.org/10.13069/jacodesmath.729440

Öz

In this work, we present a explicit trace forms for maximal real subfields of cyclotomic fields as tools for constructing algebraic lattices in Euclidean space with optimal center density. We also obtain a closed formula for the Gram matrix of algebraic lattices obtained from these subfields. The obtained lattices are rotated versions of the lattices $ \Lambda_9, \Lambda_{10}$ and $\Lambda_{11}$ and they are images of $\mathbb{Z}$-submodules of rings of integers under the twisted homomorphism, and these constructions, as algebraic lattices, are new in the literature. We also obtain algebraic lattices in odd dimensions up to $7$ over real subfields, calculate their minimum product distance and compare with those known in literatura, since lattices constructed over real subfields have full diversity.

Anahtar Kelimeler

Cyclotomic fields, Algebraic lattices, Twisted homomorphism, Signal design

Teşekkür

This work was supported by Fapesp 2013/25977-7 and CNPq 429346/2018-2.

Kaynakça

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