Trace forms of certain subfields of cyclotomic fields and applications
DOI:
https://doi.org/10.13069/jacodesmath.729440Keywords:
Cyclotomic fields, Algebraic lattices, Twisted homomorphism, Signal designAbstract
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.
Received: 7 October 2019 | Accepted: 4 December 2019Downloads
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