The asymptotic performance formula of systematic LT codes(SLT) in binary erasure channel (BEC) is firstly derived based on AND-OR tree analysis and its lower limit is given. Simulation results show that the actual bit error ratio(BER), the asymptotic performance and the lower limit match each other perfectly when the overhead is large enough. Then the optimization of degree distribution is proposed by the improved systematic linear programming(ISLP) model in accordance with the asymptotic performance. The optimized degree distribution is obviously superior to robust soliton distribution(RSD) and truncated degree distribution(TDD). Furthermore, the asymptotic behavior of the optimized degree distribution can be controlled by the given overhead and BER. In other words, the ideal BER can be obtained within the overhead we want, which also influences the overhead for complete decoding. Simulation results show that the overhead required for data recovery is close to that of we set. The comparison of BER, the overhead required for data recovery and the time of encoding and decoding for LT codes and SLT codes show that SLT codes have better performance than LT codes with more quick speed in data recovery.