第一类m子序列的构造

Construction of First Class of m Subsequences

伪随机序列在流密码、信道编码、扩频通信等领域有着广泛的应用,m序列是优秀的伪随机序列.基于m序列,本文首次提出通过重构m序列移位寄存器状态图,构造一类称之为m子序列的移位寄存器状态图.根据重构的状态图,提出了第一类m子序列并予以证明.本文推导了第一类m子序列移位寄存器反馈函数式,分析了第一类m子序列具有良好的周期特性、游程特性、平衡特性以及较高的线性复杂度.仿真结果表明,m子序列自相关特性也具有很好的δ(t)函数特征.利用文中给出的构造方法,可以构造更多性能优良的m子序列.

Pseudorandom sequence have been widly used in stream cipher, channel coding, and spread spectrum communication. m sequence is a excellent pseudorandom sequence. Based on rn sequence , we first present reconstructing it＇ s state transition diagram and gained the state transition diagram of the new sequence called m subsequence in this paper. We prove that the first class rn subsequences is existent, and present first class of m subsequences feedback functions. In the end we analyze rn subsequences properties and affirm that possess with ideal balanced property ,run property ,periodic property and good linear complexity. Statistic results show that rn subsequences autocorrelation property have δ（t） function characteristic. More new m subsequence can be obtained by using this constructing method.