We address the problem of data gathering in adhoc networks. We propose a novel framework where sensor signals are quantized and mapped to a finite field. The network nodes then combine the data from different sensors to form messages that are transmitted towards a receiver. The receiver gathers different messages and reconstructs the original signal. We study the dependence of the signal reconstruction error on the quantization and network parameters. We further compute a bound on the reconstruction error for sparse sensor signals that depends on the number of messages gathered by the receiver. We validate our results with simulations in line array and tree-based sensor networks and show that our new framework leads to effective signal reconstruction with limited transmission costs.