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## Trace forms of certain subfields of cyclotomic fields and applications

#### Agnaldo JOSÉ FERRARI [1] , Antonio APARECIDO DE ANDRADE [2] , Robson RICARDO DE ARAUJO [3] , José CARMELO INTERLANDO [4]

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.
Cyclotomic fields, Algebraic lattices, Twisted homomorphism, Signal design
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Primary Language en Engineering Articles Orcid: 0000-0002-1422-1416Author: Agnaldo JOSÉ FERRARI Institution: Sao Paulo State University (Unesp)Country: Brazil Orcid: 0000-0001-6452-2236Author: Antonio APARECIDO DE ANDRADE Institution: Sao Paulo State UniversityCountry: Brazil Orcid: 0000-0002-1357-9926Author: Robson RICARDO DE ARAUJO Institution: Sao Paulo State UniversityCountry: Brazil Orcid: 0000-0003-4928-043XAuthor: José CARMELO INTERLANDO Institution: San Diego UniversityCountry: United States This work was supported by Fapesp 2013/25977-7 and CNPq 429346/2018-2. Publication Date : May 7, 2020
 Bibtex @research article { jacodesmath729440, journal = {Journal of Algebra Combinatorics Discrete Structures and Applications}, issn = {}, eissn = {2148-838X}, address = {}, publisher = {Yildiz Technical University}, year = {2020}, volume = {7}, pages = {141 - 160}, doi = {10.13069/jacodesmath.729440}, title = {Trace forms of certain subfields of cyclotomic fields and applications}, key = {cite}, author = {José Ferrarı, Agnaldo and Aparecıdo De Andrade, Antonio and Rıcardo De Araujo, Robson and Carmelo Interlando, José} } APA José Ferrarı, A , Aparecıdo De Andrade, A , Rıcardo De Araujo, R , Carmelo Interlando, J . (2020). Trace forms of certain subfields of cyclotomic fields and applications . Journal of Algebra Combinatorics Discrete Structures and Applications , 7 (2) , 141-160 . DOI: 10.13069/jacodesmath.729440 MLA José Ferrarı, A , Aparecıdo De Andrade, A , Rıcardo De Araujo, R , Carmelo Interlando, J . "Trace forms of certain subfields of cyclotomic fields and applications" . Journal of Algebra Combinatorics Discrete Structures and Applications 7 (2020 ): 141-160 Chicago José Ferrarı, A , Aparecıdo De Andrade, A , Rıcardo De Araujo, R , Carmelo Interlando, J . "Trace forms of certain subfields of cyclotomic fields and applications". Journal of Algebra Combinatorics Discrete Structures and Applications 7 (2020 ): 141-160 RIS TY - JOUR T1 - Trace forms of certain subfields of cyclotomic fields and applications AU - Agnaldo José Ferrarı , Antonio Aparecıdo De Andrade , Robson Rıcardo De Araujo , José Carmelo Interlando Y1 - 2020 PY - 2020 N1 - doi: 10.13069/jacodesmath.729440 DO - 10.13069/jacodesmath.729440 T2 - Journal of Algebra Combinatorics Discrete Structures and Applications JF - Journal JO - JOR SP - 141 EP - 160 VL - 7 IS - 2 SN - -2148-838X M3 - doi: 10.13069/jacodesmath.729440 UR - https://doi.org/10.13069/jacodesmath.729440 Y2 - 2019 ER - EndNote %0 Journal of Algebra Combinatorics Discrete Structures and Applications Trace forms of certain subfields of cyclotomic fields and applications %A Agnaldo José Ferrarı , Antonio Aparecıdo De Andrade , Robson Rıcardo De Araujo , José Carmelo Interlando %T Trace forms of certain subfields of cyclotomic fields and applications %D 2020 %J Journal of Algebra Combinatorics Discrete Structures and Applications %P -2148-838X %V 7 %N 2 %R doi: 10.13069/jacodesmath.729440 %U 10.13069/jacodesmath.729440 ISNAD José Ferrarı, Agnaldo , Aparecıdo De Andrade, Antonio , Rıcardo De Araujo, Robson , Carmelo Interlando, José . "Trace forms of certain subfields of cyclotomic fields and applications". Journal of Algebra Combinatorics Discrete Structures and Applications 7 / 2 (May 2020): 141-160 . https://doi.org/10.13069/jacodesmath.729440 AMA José Ferrarı A , Aparecıdo De Andrade A , Rıcardo De Araujo R , Carmelo Interlando J . Trace forms of certain subfields of cyclotomic fields and applications. Journal of Algebra Combinatorics Discrete Structures and Applications. 2020; 7(2): 141-160. Vancouver José Ferrarı A , Aparecıdo De Andrade A , Rıcardo De Araujo R , Carmelo Interlando J . Trace forms of certain subfields of cyclotomic fields and applications. Journal of Algebra Combinatorics Discrete Structures and Applications. 2020; 7(2): 141-160.

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