Trace forms of certain subfields of cyclotomic fields and applications

Year 2020, Volume: 7 Issue: 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

Cited By: 1

https://izlik.org/JA54UZ95AD

Abstract

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.

Keywords

Cyclotomic fields , Algebraic lattices , Twisted homomorphism , Signal design

Thanks

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

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