Vehicle platooning has received considerable attention as a means to achieve more efficient transportation networks and vehicle autonomy. It is well known that certain systems experience undesired behaviours (instability and string instability) when the length of the platoon grows. In this context, we study homogeneous platoons of vehicles with linear dynamic models, having bi-directional communication and maintaining a constant (velocity independent) target inter vehicle spacing. We investigate both stability and string instability if the string length increases, where the vehicles utilise weighted information from multiple vehicles ahead and behind. We find conditions for the weighting factors and the linear systems that are necessary for stability of long platoons. We then show that by selecting a communication range that increases linearly with the platoon size, it is possible to achieve string stability in some cases. Further, we show that careful selection of the weighting factors can reduce the disturbance amplification considerably. (C) 2018 Elsevier Ltd. All rights reserved.