Designs, Codes and Cryptography

, Volume 73, Issue 2, pp 457–468 | Cite as

On the exact number of solutions of certain linearized equations

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Abstract

In this note we have revisited some of the results of Trachtenberg (On the cross-correlation functions of maximal linear sequences, Ph.D. thesis, University of Southern California, Los Angeles, 1970), which are directly related with the number of solutions of some special linearized polynomials over finite fields. In some cases we give improvements. Also, we give some results on the exact number of solutions of certain linearized equations depending on the coefficients of that equation.

Keywords

Linearized equations Linearized polynomials Finite fields 

Mathematics Subject Classification

12E12 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Mathematics and Institute of Applied MathematicsMiddle East Technical UniversityAnkaraTurkey
  2. 2.Department of MathematicsTOBB University of Economics and TechnologyAnkaraTurkey

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