Robson Ricardo de Araujo ; Antonio Aparecido de Andrade ; Trajano Pires da Nóbrega Neto ; Jéfferson Luiz Rocha Bastos - Constructions of well-rounded algebraic lattices over odd prime degree cyclic number fields

cm:14235 - Communications in Mathematics, March 28, 2025, Volume 33 (2025), Issue 1 - https://doi.org/10.46298/cm.14235
Constructions of well-rounded algebraic lattices over odd prime degree cyclic number fieldsArticle

Authors: Robson Ricardo de Araujo ; Antônio Aparecido de Andrade ; Trajano Pires da Nóbrega Neto ; Jéfferson Luiz Rocha Bastos

    Algebraic lattices are those obtained from modules in the ring of integers of algebraic number fields through the canonical or twisted embeddings. In turn, well-rounded lattices are those with maximal cardinality of linearly independent vectors in its set of minimal vectors. Both classes of lattices have been applied for signal transmission in some channels, such as wiretap channels. Recently, some advances have been made in the search for well-rounded lattices that can be realized as algebraic lattices. Moreover, some works have been published studying algebraic lattices obtained from modules in cyclic number fields of odd prime degree $p$. In this work, we generalize some results of a recent work of Tran et al. and we provide new constructions of well-rounded algebraic lattices from a certain family of modules in the ring of integers of each of these fields when $p$ is ramified in its extension over the field of rational numbers.


    Volume: Volume 33 (2025), Issue 1
    Published on: March 28, 2025
    Accepted on: March 14, 2025
    Submitted on: September 10, 2024
    Keywords: Mathematics - Number Theory

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