Some constructions of unimodular lattices via totally real subfields of the $p$-th cyclotomic field

Source abstract

Algebraic number theory has recently attracted significant interest due to its role in algebraic lattice theory and in the design of codes for applications in coding theory. Algebraic lattices have been useful in information theory, where the problem of constructing lattices over number fields with full diversity and maximal minimum product distance has been investigated, since these parameters are directly related to error probabilities over Rayleigh fading channels. In this paper, we present a family of full diversity rotated unimodular lattices constructed via totally real subfields of the cyclotomic fields $\mathbb{Q}(\zeta_p)$, with $p$ an odd prime. A closed-form expression for the minimum product distance is derived.Accepted: 20 September 2025