极长D序列的游程分布

The Distribution of Runs for Maximum-LengthD Sequences

本文讨论了GF(2)上D序列的伪随机性,得到了GF(2)上极长D序列游程分布的一般规律。给出了其总游程个数及k长游程个数的计算公式,证明了在极限情况下,k长游程个数是总游程个数的1/2~k。最后分析了D序列的最大游程与离散对数之间的关系。

In this paper, we discribe the pseudorandom property of decimal sequences over GF(2), We obtain the general rule of the distribution of runs for maximum-lengtth D sequences, in base two. The formulas to calculate the numbers of whole runs and that of k-length runs are given. It is proved that the distribution of runs for maximum-length D sequences becomes closer to the requirement for pseudorandom numbers as q increase. Finally, the relation between maximum length runs of D sequences and discrete logarithms is also analysed.