In this paper we introduce a novel linear network coding scheme, namely “rotate-and-add coding”, that possesses low encoding complexity and operates fundamentally different from the traditional network codes. This scheme can operate on a small field (e.g. F ₂ ), thereby, it alleviates the computational complexities due to multiplication and addition operations in large finite fields. The key idea is to function on a vector of symbols instead of working with a single symbol of a large field. Each node encodes its received vectors by simply rotationally shifting the vectors and then adding them, i.e., here the addition is done in vector form and the multiplication is replaced by rotation. We verify that the new scheme requires lower computation and overhead than the existing schemes. However, as the cost of reducing the complexity, it provides slightly smaller throughput.