Abstract
The almost perfect binary sequences have been defined in [6] as (−1, +1)-periodic sequences such that all their out-of-phase autocorrelation coefficients are zero except one. In the preceding paper, the study of the almost perfect binary sequences is done by means of the ringF 2[X]/(X n−1). Here, the arithmetic of cyclotomic fields enables us to solve open problems and questions like: structure and existence of these sequences.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Baumert, L. D.: Cyclic Difference Sets. Lecture Notes in Mathematics, vol.182, Berlin, Heidelberg, New York: Springer 1971
Birch, B. J.: Cyclotomic Fields and Kummer Extensions. In: Algebraic Number Theory. New York: Academic Press 1967
Ireland, K., Rosen, M.: A Classical Introduction to Modern Number Theory. Graduate Texts in Mathematics, vol.84, Berlin, Heidelberg, New York: Springer 1990
Kumar, P. V., Scholtz, R. A., Welch, L. R.: Generalized bent functions and their properties. J.C.T, Series A40, 90–107 (1985)
Samuel, P.: Théorie Algébrique des Nombres. Paris: Hermann 1967
Wolfmann, J.: Almost perfect auto-correlation sequences. IEEE Trans. Inform.38, (4) July 1992
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Langevin, P. Almost perfect binary functions. AAECC 4, 95–102 (1993). https://doi.org/10.1007/BF01386833
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01386833