Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지
DOI QR코드

DOI QR Code

THE NUMBER OF SOLUTIONS TO THE EQUATION (x + 1)d = xd + 1

  • Yim, Ji-Mi (Department of Applied Mathematics, Pukyong National University) ;
  • Cho, Sung-Jin (Department of Applied Mathematics, Pukyong National University) ;
  • Kim, Han-Doo (Institute of Basic Science and Department of Computer Aided Science, Inje University) ;
  • Choi, Un-Sook (School of Free Major, Tongmyoung University) ;
  • Choi, Ji-Youn (Department of Applied Mathematics, Pukyong National University)
  • Received : 2012.09.06
  • Accepted : 2012.11.15
  • Published : 2013.01.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we study the number of solutions to the equation $(x+1)^d=x^d+1$. This equation gives the value of the third power sum equation in case of Niho type exponents and is helpful in finding the distribution of the values $C_d({\tau})$. We provide the number of the solutions using the new method.

Keywords

References

  1. H. Dobbertin, Almost perfect nonlinear power functions on GF($2^n$):the Welch case, IEEE Transactions on Information Theory, 45(4):1271-1275, 1999. https://doi.org/10.1109/18.761283
  2. S.W. Golomb, Shift register sequences, Discrete Mathematics, Holden Day, 1967.
  3. Han-Doo Kim and Sung-Jin Cho, A new proof about the decimations with Niho type five- valued cross-correlation functions, J. Appl. Math. and Informatics, 30(5-6):903-911, 2012. https://doi.org/10.14317/JAMI.2012.30.5_6.903
  4. T. Helleseth, Some results about the cross-correlation function between two maximal linear sequences, Discrete Mathematics, 16(3):209-232, 1976. https://doi.org/10.1016/0012-365X(76)90100-X
  5. R. Lidl and H. Niederreiter, Finite fields, Cambridge University Press, 1997.
  6. R. McEliece, Finite fields for computer scientists and engineers, Kluwer Academic Publishers, Boston, 1987.
  7. G. McGuire, On certain 3-weight cyclic codes having symmetric weights and a conjecture of Helleseth, In Sequences and their applications(Bergen, 2001), Discrete Math. Theor. Comput. Sci. (Lond.), pages 281-295. Springer, London, 2002.
  8. Y. Niho, Multi-valued cross-correlation functions between two maximal linear recursive sequences, Ph.D thesis, University of Southern California, 1972.
  9. P. Rosendahl, Niho type cross-correlation functions and related equations, Ph.D thesis, Turku center for computer science, 2004.

Cited by

  1. Analysis of Cross-correlation Frequency between Non-linear Binary Sequences Family with 5-Valued Cross-Correlation Functions vol.17, pp.12, 2013, https://doi.org/10.6109/jkiice.2013.17.12.2875