A Three-Valued Walsh Transform From Decimations of Helleseth–Gong Sequences

摘要

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.