Abstract
Both R. Games [4] and V.P. Ipatov [8] have given constructions for perfect ternary sequences. Games uses difference sets and quadrics in projective space, while Ipatov uses q-ary m-sequences. We show that the Ipatov sequences are a subset of the Games sequences. Further, we show that a conjecture of Games relating to quadrics in projective spaces does not hold in general.
Similar content being viewed by others
References
L.D. Baumert, Cyclic Difference Sets, Springer-Verlag, Berlin, (1971).
Th. Beth, D. Jungnickel, and H. Lenz, Design Theory, Bibliographisches Institut, Zurich, (1985).
J. Dieudonné, Sur le groupes classiques, Hermann, Paris, (1967).
R.A. Games, The geometry of quadrics and correlations of sequences, IEEE Trans. on Inform. Theory, Vol. 32 (1986), pp. 423–426.
J.W.P. Hirschfeld, Projective Geometries over Finite Fields, Clarendon Press, Oxford, (1979).
T. Høholdt and J. Justesen, Ternary sequences with perfect periodic autocorrelation, IEEE Trans. on Inform. Theory, Vol. 29 (1983), pp. 597–600.
D.R. Hughes and F.C. Piper, Design Theory, Cambridge University Press, Cambridge, (1985).
V.P. Ipatov, Ternary sequences with ideal periodic autocorrelation properties, Radio Engin. Electron. Physics, Vol. 24 (1979), pp. 75–79.
E.J.F. Primrose, Quadrics in finite geometries, Proc. Camb. Phil. Soc., Vol. 47 (1951), pp. 299–304.
D. Shedd and D.V. Sarwate, Construction of sequences with good correlation properties, IEEE Trans. on Inform. Theory, Vol. 25 (1979), pp. 94–97.
Author information
Authors and Affiliations
Additional information
Communicated by G.J. Simmons
Rights and permissions
About this article
Cite this article
Jackson, W.A., Wild, P.R. Relations between two perfect ternary sequence constructions. Des Codes Crypt 2, 325–332 (1992). https://doi.org/10.1007/BF00125201
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00125201