Your browser does not support JavaScript!

Two constructions of binary sequences with optimal autocorrelation magnitude

Two constructions of binary sequences with optimal autocorrelation magnitude

For access to this article, please select a purchase option:

Buy article PDF
(plus tax if applicable)
Buy Knowledge Pack
10 articles for $120.00
(plus taxes if applicable)

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Your details
Why are you recommending this title?
Select reason:
Electronics Letters — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

In this Letter, two constructions of new binary sequences with optimal autocorrelation magnitude of length 4N derived from binary sequences with optimal autocorrelation of length N = 2 (mod 4) and almost-perfect binary sequences of length 2N using N × 2 interleaved structure is presented. The first construction is to use binary Sidelnikov sequences of length N = pn −1 whereas the second one is to use binary Ding–Helleseth–Martinsen sequences of length N = 2p. The obtained sequences have large linear complexity and can be used in communication and cryptography.


    1. 1)
      • 7. Sidelnikov, V.M.: ‘Some k-valued pseudo-random sequences and nearly equidistant codes’, Probl. Inf. Transm., 1969, 5, (1), pp. 1216.
    2. 2)
    3. 3)
      • 6. Ding, C., Helleseth, T., Lam, K.Y.: ‘Several classes of binary sequences with three-level autocorrelation’, IEEE Trans. Inf. Theory, 1999, 44, (7), pp. 26012606, doi: 10.1109/18.796414.
    4. 4)
    5. 5)
      • 13. Yan, S.Y.: ‘Number theory for computing’ (Springer-Verlag, Berlin, Heidelberg, 2002, 2nd edn.).
    6. 6)
      • 14. Helleseth, T., Yang, K.: ‘On binary sequences n = pm−1 with optimal autocorrelation’. SETA '01, Discrete Mathematics and Theoretical Computer Science, Bergen, Norway, May 2001, pp. 209217, doi: 10.1007/978-1-4471-0673-9.
    7. 7)
    8. 8)
      • 2. Golomb, S.W., Gong, G.: ‘Signal design for good correlation - for wireless communication, cryptography and radar’ (Cambridge University Press, USA, 2005).
    9. 9)
      • 1. Fan, P., Darnell, M.: ‘Sequence design for communications applications’ (Research Studies Press Ltd., England, London, 1996).
    10. 10)
      • 15. Berlecamp, E.R.: ‘Algebraic coding theory’ (McGraw-Hill, Inc., New-York, 1968).
    11. 11)
    12. 12)
    13. 13)
    14. 14)
      • 8. Arasu, K.T.: ‘Sequences and arrays with desirable correlation properties’ inCrnković, D., Tonchev, V. (Eds.): ‘Information Security, Coding Theory and Related Combinatories’ (the authors and IOS Press, USA and Canada, 2011, doi: 10.3233/978-1-60750-663-8-136).
    15. 15)

Related content

This is a required field
Please enter a valid email address