Construction of Complex Lattice Codes via Cyclotomic Fields

Authors

  • E. D. Carvalho UNESP/Ilha Solteira
  • A. A. Andrade UNESP/São José do Rio Preto
  • T. Shah University of Quaid-i-Azam
  • C. C. Trinca Federal University of Tocantins

DOI:

https://doi.org/10.5540/tcam.2022.023.01.00033

Abstract

Through algebraic number theory and Construction $A$ we extend an algebraic procedure which generates complex lattice codes from the polynomial ring \mathbb{F}_{2}[x]/(x^{n}-1), where \mathbb{F}_{2}=\{0,1\}, by using ideals from the generalized polynomial ring \frac{\mathbb{F}_{2}[x,\frac{1}{2}\mathbb{Z}_{0}]}{((x^{\frac{1}{2}})^{n}-1)} through the ring of integers $\mathcal{O}_{\mathbb{L}}$ of the cyclotomic field \mathbb{L}=\mathbb{Q}(\zeta_{2^{s}}), where \zeta_{2^{s}} is a 2^{s}-th root of the unit, with s>2.

Downloads

Published

2022-03-25

How to Cite

Carvalho, E. D., Andrade, A. A., Shah, T., & Trinca, C. C. (2022). Construction of Complex Lattice Codes via Cyclotomic Fields. Trends in Computational and Applied Mathematics, 23(1), 33–50. https://doi.org/10.5540/tcam.2022.023.01.00033

Issue

Vol. 23 No. 1 (2022)

Section

Original Article

License

Authors who publish in this journal agree to the following terms: 

  1. Authors retain copyright and grant the journal the right of first publication, with the work simultaneously licensed under the Creative Commons Attribution License that allows the sharing of the work with acknowledgment of authorship and initial publication in this journal.

  2. Authors are authorized to assume additional contracts separately, for non-exclusive distribution of the version of the work published in this journal (eg, publish in an institutional repository or as a book chapter), with acknowledgment of authorship and initial publication in this journal.
     

  3. Authors are allowed and encouraged to publish and distribute their work online (eg, in institutional repositories or on their personal page) at any point before or during the editorial process, as this can generate productive changes as well as increase impact and the citation of the published work (See The effect of open access).

  4. This is an open access journal which means that all content is freely available without charge to the user or his/her institution. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles, or use them for any other lawful purpose, without asking prior permission from the publisher or the
    author. This is in accordance with the BOAI definition of open access

 

Intellectual Property

All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License under attribution BY.