Orthogonal Residue Sequences
This paper presents a class of random orthogonal sequences associated with the number theoretic Hilbert transform. We present a constructive procedure for finding the random sequences for different modulus values. These random sequences have autocorrelation function that is zero everywhere excepting at the origin. These sequences may be used as keys in communication applications in a manner that is analogous to the use of PN sequences in spread spectrum systems.
KeywordsRandom sequences Orthogonal sequences Number theoretic Hilbert transform Key distribution Code division
This research was supported in part by the National Science Foundation Grant CNS-1117068.
- 1.R. Al-Aifari, A. Katsevich, Spectral analysis of the truncated Hilbert transform with overlap (2013) http://arxiv.org/abs/1302.6295
- 4.N.S. Jayant, S. Kak, Uniform permutation privacy system, US Patent No. 4,100, 374, July 11, (1978)Google Scholar
- 12.R. Kandregula, The basic discrete Hilbert transform with an information hiding application. (2009) http://arxiv.org/abs/0907.4176
- 14.V.K. Kotagiri, New results on the number theoretic Hilbert transform. (2013) http://arxiv.org/abs/1310.6924