This paper presents a procedure for synthesis of linear test pattern generators called SLING. SLING can synthesize linear test pattern generators that satisfy constraints on area, speed, internal fan out, and randomness properties and outperform existing linear test pattern generator designs including linear feedback shift registers (LFSRs) and cellular automatons (CAs). SLING is a constraint-driven synthesis procedure that takes as input a set of constraints and then synthesizes a test pattern generator that satisfies those constraints. SLING uses a set of linear transformations that it applies iteratively to evolve a linear test pattern generator. Because of the way the transformations are chosen and constraints are set, a high degree of phase shift is maintained between every pair of linear sequences generated at different bit positions of the generator and cross and auto correlations are highly minimized. Hardware overhead in terms of XOR gates is also minimized. Comparative analysis and experimental results show the effectiveness of the proposed synthesis scheme