A Three-Valued Walsh Transform From Decimations of Helleseth-Gong Sequences
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.
walsh transform autocorrelation p-ary sequences m-sequences cross-correlation