中文摘要：

有限域GF（2’上本原σ-LFSR序列的分量序列均是二元域上具有相同极小多项式的m-序列，已知一条GF（2勺上本原cr-LFSR序列的距离向量，就可以用二元域上的m-序列构造它．研究了一类本原cr-LFSR序列-Z本原σ-LFSR序列距离向量的计算问题．给出了一种GF（2k）上n级Z本原σ-LFSR序列距离向量的计算方法，其主要思想是-并U用GF（2k）上1级z本原σ-LFSR序列的距离向量来计算n级z本原σ-LFSR序列的距离向量与其他现有方法相比，该方法的效率更高．更有价值的是，该方法也适用于GF（2b上n级m．序列距离向量的计算．最后给出了GF（2k）上n级z本原σ-LFSR序列的计数公式，说明其个数比GF（2k）上n级m-序列更多．

英文摘要：

The coordinate sequences of a primitive σ-LFSR sequence over GF（2k） are m-sequences with the same minimal polynomial over GF（2）, thus a primitive σ-LFSR sequence over GF（2k） can be constructed by m-sequences over GF（2） if its interval vector is known. This paper studies the calculation of interval vectors of a class of primitive σ-LFSR sequences--Z primitive σ-LFSR sequences and presents an improved method to calculate the interval vectors of Z primitive σ-LFSR sequences in order n over GF（2k）, which uses the interval vectors of Z primitive σ-LFSR sequences of order 1 to calculate that of Z primitive σ-LFSR sequences in order n over GF（2k）. In addition, it is more effective than other existing methods. More importantly, the new method can also be applied to the calculation of interval vectors of m-sequences over GF（2k）. The enumeration formula of Z primitive σ-LFSR sequences of order n over GF（2k） is also presented, which shows that the number of Z primitive σ-LFSR sequences of order n is much larger than the number of m-sequences of order n over GF（2k）.