Tire with a radial or cross-ply carcass

A tire comprising at least one carcass reinforcement radially inside a belt reinforcer comprising a first and a second transverse end, the belt reinforcer being radially inside a tread, the belt reinforcer comprising the following distinct elements:

• a reinforcing ply, having a transverse half-width L2, comprising a polymer reinforcing layer positioned between two layers of coating rubber, the polymer layer being in the form of strips,
• at least one hooping ply, having a transverse half-width L1, and comprising filamentary reinforcing elements, parallel two by two, forming at most an angle at most equal to 7° with respect to the circumferential direction of the tire, the at least one hooping ply surmounting the reinforcing ply,
• wherein the tire comprises at least one layer of edge uncoupling rubber, positioned at least radially between the hooping ply and the reinforcing ply and positioned at at least one transverse end of the belt reinforcer, the layer of edge uncoupling rubber having a total length between 10 and 40 mm and a thickness between 0.2 and 1.2 mm, and comprising at least one reinforcing ply, wherein at at least one end of the belt reinforcer, the half-widths L1 and L2 are different, and manifest a difference (L1−L2) between 5 and 10 mm, and
• wherein each layer of coating rubber of the polymer reinforcing layer has a secant modulus at 10% elongation, denoted Ms, greater than or equal to 30 MPa.