二元周期序列的计数

以组合计数理论为基础，推导出特殊序列（自互反序列和自互补序列）计数公式和排除等价序列（互反、互补序列）后的本原周期序列计数公式，使搜寻可用序列的基序列数目约缩为原来的１／４，进一步，应用Ｓｔｉｒｌｉｎｇ浙近公式求出当周期较大时各种特殊序列数目的的比例关系，所导出的公式不仅完善了公用控制的设计理论，而且使长周期可用序列的搜寻工作量减少到近１／４。

Counting of Binary Cyclic Sequences

Based on the combinatorial counting theory,the formulae of enumeration of such special binary cyclic sequences as self-mutual reverse sequences and self-complementary sequences,and that of primitive cyclic sequences after removing equivalent sequences are deduced so that the work of calculations can be reduced nearly four times. Further,the proportional relationships of the numbers of the special sequences of long periods are derived by applying Stirling's formula of asymptotic enumeration. All the formulae of enumeration not only perfect the theory of design of shared controllers but also reduce the computing work for usable sequences of long periods by three-fourths.