摘要： 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。

关键词: 序列, 广义割圆类, 自相关值

Abstract: 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.

Key words: sequence, generalized cyclotomic classes, autocorrelation values

中图分类号: 

• TP309