摘要
Based on the quadratic exponential method, this paper constructs two types of generators over finite field Fq, the digital quadratic exponential generator and quadratic exponential pseudorandom vector generator. We investigate the distribution of the sequence generated by the generators, and present results about their one dimensional discrepancy. The proofs are based on the estimate of certain character sum over Fq. Ift is the least period of the sequence and t≥q^1/2＋2c, then the bound of the discrepancy is O（t^-1/4q^1/8＋τ logq） for any ε 〉 0. It shows that the sequence is asymptotically uniformly distributed.
Based on the quadratic exponential method, this paper constructs two types of generators over fi-nite field Fq , the digital quadratic exponential generator and quadratic exponential pseudorandom vector gen-erator. We investigate the distribution of the sequence generated by the generators, and present results about their one dimensional discrepancy. The proofs are based on the estimate of certain character sum over Fq .If t is the least period of the sequence and t ≥ q1 /2 +2 ε,then the bound of the discrepancy is O (t ? 1/4 q1 /8+ εlog q)for any ε > 0.It shows that the sequence is asymptotically uniformly distributed.
基金
Supported by the Special Fund of National Excellent Doctoral Dissertation (Grant 200060) and the National Natural Science Foundation of China (No.60373092).
