Title :
A Three-Valued Walsh Transform From Decimations of Helleseth–Gong Sequences
Author :
Gong, Guang ; Helleseth, Tor ; Hu, Honggang
Author_Institution :
Dept. of Electr. & Comput. Eng., Univ. of Waterloo, Waterloo, ON, Canada
Abstract :
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.
Keywords :
sequences; sequential codes; transforms; Helleseth-Gong sequence decimation; p-ary m-sequences; three-valued Walsh transform; two-level autocorrelation sequence; Awards activities; Correlation; Cryptography; Educational institutions; Information theory; Transforms; Vectors; $m$-sequences; $p$-ary sequences; Autocorrelation; Walsh transform; cross-correlation;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2011.2169297
