Designs, Codes and Cryptography

, Volume 4, Issue 3, pp 327–340

On sequences with zero autocorrelation

  • C. Koukouvinos
  • S. Kounias
  • J. Seberry
  • C. H. Yang
  • J. Yang
Article

DOI: 10.1007/BF01388649

Cite this article as:
Koukouvinos, C., Kounias, S., Seberry, J. et al. Des Codes Crypt (1994) 4: 327. doi:10.1007/BF01388649
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Abstract

Normal sequences of lengthsn=18, 19 are constructed. It is proved through an exhaustive search that normal sequences do not exist forn=17, 21, 22, 23. Marc Gysin has shown that normal sequences do not exist forn=24. So the first unsettled case isn=27.

Base sequences of lengths 2n−1, 2n−1,n,n are constructed for all decompositions of 6n−2 into four squares forn=2, 4, 6, ..., 20 and some base sequences forn=22, 24 are also given. So T-sequences (T-matrices) of length 71 are constructed here for the first time. This gives new Hadamard matrices of orders 213, 781, 1349, 1491, 1633, 2059, 2627, 2769, 3479, 3763, 4331, 4899, 5467, 5609, 5893, 6177, 6461, 6603, 6887, 7739, 8023, 8591, 9159, 9443, 9727, 9869.

Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • C. Koukouvinos
    • 1
  • S. Kounias
    • 2
  • J. Seberry
    • 3
  • C. H. Yang
    • 4
  • J. Yang
    • 5
  1. 1.Department of MathematicsNational Technical University of AthensAthensGreece
  2. 2.Department of MathematicsUniversity of AthensPanepistemiopolisGreece
  3. 3.Department of Computer ScienceUniversity of WollongongWollongongAustralia
  4. 4.Department of Mathematical SciencesState University of New YorkOneontaUSA
  5. 5.Department of Computer Science and Computer Science Division of Electrical EngineeringUniversity of CaliforniaBerkeleyUSA

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