Lattices are discrete additive subgroups of \(\mathbb {R}^n\) known to be useful in finding solutions to important mathematical problems, such as the Sphere Packing Problem, and in applications for coding theory and post-quantum cryptography. In particular, well-rounded lattices have been considered for data transmission on Wiretap channels. A lattice obtained as an image of a free \(\mathbb {Z}\) -submodule of the ring of algebraic integers of a number field through the canonical embedding, or a twisted version of it, is called an algebraic lattice. In 2012, Fukshansky and Petersen showed that an algebraic lattice obtained as image of the whole ring of algebraic integers of a number field \(\mathbb {K}\) through the canonical embedding is well-rounded if and only if \(\mathbb {K}\) is a cyclotomic field. In this work, we prove that the lattice obtained as image of the ring of algebraic integers of the maximal real subfield of the 4q-th cyclotomic field via some twisted embedding is well-rounded for any odd integer number q.
