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.