A Three-Valued Walsh Transform From Decimations of Helleseth–Gong Sequences
A Three-Valued Walsh Transform From Decimations of Helleseth–Gong Sequences
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DOI：
10.1109/tit.2011.2169297
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发表时间：
2012-02
影响因子：
2.5
通讯作者：
G. Gong;T. Helleseth;Honggang Hu
中科院分区：
文献类型：
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作者：
G. Gong;T. Helleseth;Honggang Hu
两级自相关序列的沃尔什变换在任意两个序列正交的序列集合的构造中发挥了重要作用。对于 p 元序列，对于任意奇素数 p，只有两个基本类的两级自相关序列，没有子域结构。一类是p元m序列类，另一类是p元Helleseth-Gong序列类。在本文中，p-ary Helleseth-Gong序列的子类的沃尔什变换及其特定抽取的沃尔什变换被完全确定并且被证明是三值的。
The Walsh transform of two-level autocorrelation sequences has played an important role in the construction of the set of sequences in which any two sequences are orthogonal. For p -ary sequences, there are only two basic classes of two-level autocorrelation sequences with no subfield structures for an arbitrary odd prime p. One is the class of p-ary m-sequences and the other is the class of p -ary Helleseth-Gong sequences. In this paper, the Walsh transform of a subclass of p -ary Helleseth-Gong sequences and the Walsh transform of their particular decimations are completely determined and are shown to be three-valued.