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- Title
Trace forms of certain subfields of cyclotomic fields and applications.
- Authors
José Ferrari, Agnaldo; Aparecido de Andrade, Antonio; Ricardo de Araujo, Robson; Carmelo Interlando, José
- 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 Λ9;Λ10 and Λ11 and they are images of 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.
- Subjects
CYCLOTOMIC fields; RINGS of integers; HOMOMORPHISMS; DIMENSION theory (Algebra); BOOLEAN functions
- Publication
Journal of Algebra Combinatorics Discrete Structures & Applications, 2020, Vol 7, Issue 2, p141
- ISSN
2148-838X
- Publication type
Article
- DOI
10.13069/jacodesmath.729440