Description of the class of probability measures on the group ${\mathbb Z}_2^3$ that have a trivial equivalence class

TL;DR

This paper characterizes probability measures on the group ${ m Z}_2^3$ that are uniquely identified by the modulus of their characteristic function, up to a shift, providing a complete classification.

Contribution

It offers a complete description of measures on ${ m Z}_2^3$ with trivial equivalence classes based on their characteristic functions.

Findings

Characterization of measures with trivial equivalence classes

Unique determination by characteristic function modulus

Complete classification of such probability measures

Abstract

A complete description is given of the class of probability measures on the group ${\mathbb Z}_2^3$, which are uniquely determined by the modulus of their characteristic function up to a shift.