扩展的WG序列线性复杂度的研究

On the Linear Span of the Extended WG Sequences

Welch-Gong(WG)序列是一类具有良好随机性的二元序列,由特定的五项式通过WG变换产生.文章将WG变换中特定的五项式推广成一般的三项式,对基于三项式的WG序列的线性复杂度展开研究,找到了几类指数的一般形式,能使序列的线性复杂度为指数级增长,为三项式在WG变换中的应用提供了多种选择.

Welch-Gong（WG） sequences have good randomness. The original WG sequences are generated by a specific five-term function through WG transformation. This paper extends the specific five-term function to general three-term function in WG transformation, and studies the linear span of WG sequences based on three-term function. Some general forms of the indexes, which can make linear span increase exponentially are found. This provides a variety of options for the applications of three-term function in the WG transformation.