Helleseth-Gong序列的采样的Hadamard变换性质研究

摘要

According to the spectrum analysis method,the Hadamard transform of a new family of nonbinary sequences of period pn-1 with symbols from a finite field Fp for any prime p ＞ 2 was studied.Such sequences had ideal two-level autocorrelation.The Hadamard transform values were determined and shown to be three-valued,and the construction of Helleseth-Gong sequences was modified.Furthermore,the relationship between the Hadamard transform and the Walsh transform for the particular function was found.%对于具有理想二级自相关函数,周期为pn-1的Helleseth-Gong序列,利用频谱分析的方法研究其Hadamard 变换的性质,并证明其Hadamard变换是三值的.完善了Helleseth-Gong序列的构造,同时证明了对于特殊序列的Walsh变换和Hadamard变换之间的关系.