I don't think you mean dump pipe (wastegate), where the length is meaningless unless it was a major restriction.
I think you meant down pipe, which is after the outlet of the turbine. The best solution is no pipe at all, which offers the least restriction - to flow, not pressure change. This is usually not practical, so the shortest length that carries the heat away is best, and the diameter should be designed to carry the heat away quickly. There is no useful "pulse train" or scavenging effect post-turbo, so the largest diameter that maximizes exhaust velocity without cooling (which slows the exhaust and creates backpressure reducing flow) is desired. The effects of a installing a cat-back or turbo-back large diameter "unrestricted" exhaust system are quite minimal on a turbosupercharged application, compared to a NA engine. There are even high-performance downpipes that incorporate catalytic converters, with very little performance loss. The largest source of backpressure in any turbosupercharged system will always be the turbo itself.
It's a common misconception that the vanes are motivated by mere pressure. Solar Mike is quite correct; it is the expansion of the incredibly hot exhaust gas that motivates the turbine. The majority of the energy comes from the heat, not the pressure. Hypothetically, if the exhaust gas was at ambient temperature, the turbine would barely spin, and certainly not have enough momentum to drive the compressor wheel.
"Maximum Boost: Designing, Testing and Installing Turbocharger Systems" by Corky Bell is my go-to bible on this subject, even though it's a bit old. The physics, however, hasn't changed.
Enthalpy: a thermodynamic quantity equivalent to the total heat
content of a system. It is equal to the internal energy of the system
plus the product of pressure and volume.
Increasing inlet pressure on the inlet of the turbine has the negative effect of restricting cylinder exhaust flow, and decreasing the volumetric efficiency of the engine. Increasing (or conserving) the heat, and possibly improving the volume (bigger valves, cam profile, etc) are the opportunities to generate more power in turbo applications. This is why you often see the exhaust manifold wrapped in insulation.