Rotated $D_n$-lattices in dimensions power of 3

Agnaldo J. Ferrari; Grasiele C. Jorge; Antonio A. De Andrade

Rotated $D_n$-lattices in dimensions power of 3

Abstract

In this work, we present constructions of families of rotated $D_n$-lattices which may be good for signal transmission over both Gaussian and Rayleigh fading channels. The lattices are obtained as sublattices of a family of rotated $\mathbb{Z} \oplus \mathcal{A}_{2}^{k}$ lattices, where $\mathcal{A}_{2}^{k}$ is a direct sum of $k=\frac{3^{r-1}-1}{2}$ copies of the $A_2$-lattice, using free $\mathbb{Z}$-modules in $\mathbb{Z}[\zeta_{3^{r}}+\zeta_{3^{r}}^{-1}]$.

Keywords

References

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Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Authors

Agnaldo J. Ferrari ^* This is me
0000-0002-1422-1416
Brazil

Grasiele C. Jorge This is me
0000-0002-1474-6001
Brazil

Antonio A. De Andrade This is me
Brazil

Publication Date

September 15, 2021

Submission Date

May 15, 2020

Acceptance Date

May 15, 2021

Published in Issue

Year 2021 Volume: 8 Number: 3

IZ

https://izlik.org/JA62UN88ZS

Cite

RIS / Bibtex

APA

Ferrari, A. J., Jorge, G. C., & De Andrade, A. A. (2021). Rotated $D_n$-lattices in dimensions power of 3. Journal of Algebra Combinatorics Discrete Structures and Applications, 8(3), 151-160. https://izlik.org/JA62UN88ZS

AMA

1.Ferrari AJ, Jorge GC, De Andrade AA. Rotated $D_n$-lattices in dimensions power of 3. Journal of Algebra Combinatorics Discrete Structures and Applications. 2021;8(3):151-160. https://izlik.org/JA62UN88ZS

Chicago

Ferrari, Agnaldo J., Grasiele C. Jorge, and Antonio A. De Andrade. 2021. “Rotated $D_n$-Lattices in Dimensions Power of 3”. Journal of Algebra Combinatorics Discrete Structures and Applications 8 (3): 151-60. https://izlik.org/JA62UN88ZS.

EndNote

Ferrari AJ, Jorge GC, De Andrade AA (September 1, 2021) Rotated $D_n$-lattices in dimensions power of 3. Journal of Algebra Combinatorics Discrete Structures and Applications 8 3 151–160.

IEEE

[1]A. J. Ferrari, G. C. Jorge, and A. A. De Andrade, “Rotated $D_n$-lattices in dimensions power of 3”, Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 8, no. 3, pp. 151–160, Sept. 2021, [Online]. Available: https://izlik.org/JA62UN88ZS

ISNAD

Ferrari, Agnaldo J. - Jorge, Grasiele C. - De Andrade, Antonio A. “Rotated $D_n$-Lattices in Dimensions Power of 3”. Journal of Algebra Combinatorics Discrete Structures and Applications 8/3 (September 1, 2021): 151-160. https://izlik.org/JA62UN88ZS.

JAMA

1.Ferrari AJ, Jorge GC, De Andrade AA. Rotated $D_n$-lattices in dimensions power of 3. Journal of Algebra Combinatorics Discrete Structures and Applications. 2021;8:151–160.

MLA

Ferrari, Agnaldo J., et al. “Rotated $D_n$-Lattices in Dimensions Power of 3”. Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 8, no. 3, Sept. 2021, pp. 151-60, https://izlik.org/JA62UN88ZS.

Vancouver

1.Agnaldo J. Ferrari, Grasiele C. Jorge, Antonio A. De Andrade. Rotated $D_n$-lattices in dimensions power of 3. Journal of Algebra Combinatorics Discrete Structures and Applications [Internet]. 2021 Sep. 1;8(3):151-60. Available from: https://izlik.org/JA62UN88ZS