The use of a certain copolymer is described for reducing the gas-permeability of rubber material. A rubber material provided with a barrier material in the form of the copolymer is also described. The copolymer can be produced via ring-opening metathesis polymerization of a) one first olefin monomer selected from the group consisting of cyclic olefin monomers having at least one endocyclic C—C double bond, where no tertiary carbon atom bearing a hydrogen atom is present in alpha-position to the double bond, and b) one second olefin monomer selected from the group consisting of cyclic olefin monomers having one endocyclic C—C double bond, where a tertiary carbon atom bearing a hydrogen atom is present in at least one alpha-position to the double bond, where the copolymer has been oxidized at least to some extent, where the amount of polycyclic olefin monomers used to produce the copolymer with at least two C—C double bonds is zero or less than 1 mol %, based on the entirety of the monomers.