阶数为2的pq周期广义割圆序列的自相关值

Autocorrelation Values of New Generalized Cyclotomic Sequences of Order Two of Length pq

给出了关于阶数为2的pq周期广义割圆序列自相关值的几个猜想,这类序列是由Ding和Helleseth构造的,大量的实验结果验证了猜想的正确性,但没有找到理论证明的方法。结果表明这类序列的自相关值为5-,4-或3-值,序列具有"好"的自相关性质,而且这类序列也具有大的线性复杂度,可以作为流密码中的密钥流序列或作为随机数发生器。

This paper gives some conjectures on the autocorrelation values of new generalized cyclotomic sequences of order 2 of length pq defined by Ding and Helleseth.The results show that the autocorrelation functions of these sequences are 5-,4-or 3-valued.These sequences have good autocorrelation property.The conjectures come from a computer programm which compute the autocorrelation values.All tested examples confirme to these conjectured values and so these assumptions appear to be well founded.However,a theoretical confirmation is not yet forthcoming.These sequences also have large linear complexity,which make it possible as key stream in stream ciphers or as random number generators.