Not by themselves. Earnshaw's theorem shows that no arrangement of static permanent magnets can hold an object in stable levitation. Push two repelling magnets together and, unless something stops them, they slide sideways or flip over.
Correlated Magnetics Research addresses this directly on its FAQ. With a light mechanical constraint that stops lateral movement, a repelling pair will appear to hover; CMR calls this its spring function. It says two axes must be constrained for many of its functions, including the spring, to work. Magnetic bearing systems are possible, CMR says, as long as part of the system is held apart mechanically.
Patterned magnets also do not create frictionless motion or free energy. The mechanical constraint still has friction, and CMR states it will not accept custom design requests for levitation, frictionless-motion or free-energy projects.
What coded magnets can usefully do here is provide a contactless spring: a pair that rests a set distance apart and returns there when pushed or pulled. CMR's spring design note adds that the pair damps vibration between the two parts, which can be tuned for a specific mass and frequency range.
WholeMagnetics, 2026-10-04. Polymagnet facts are taken from Correlated Magnetics Research’s public pages, listed below; vendor performance figures are CMR’s own.