Generalized nonbinary sequences with perfect autocorrelation, flexible alphabets and new periods


BOZTAŞ S., ÖZBUDAK F., TEKİN E.

CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES, vol.10, no.3, pp.509-517, 2018 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 10 Issue: 3
  • Publication Date: 2018
  • Doi Number: 10.1007/s12095-017-0237-6
  • Journal Name: CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.509-517
  • Keywords: Feedback shift registers, Sequences, Autocorrelation, Finite fields

Abstract

We extend the parameters and generalize existing constructions of perfect autocorrelation sequences over complex alphabets. In particular, we address the PSK+ constellation (Boztas and Udaya 2010) and present an extended number theoretic criterion which is sufficient for the existence of the new sequences with perfect autocorrelation. These sequences are shown to exist for nonprime alphabets and more general lengths in comparison to existing designs. The new perfect autocorrelation sequences provide novel alternatives for wireless communications and radar system designers for applications in ranging and synchronisation as well as channel identification.