On the exact number of solutions of certain linearized equations

ÖZBUDAK F., SAYGI Z.

DESIGNS CODES AND CRYPTOGRAPHY, vol.73, no.2, pp.457-468, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 73 Issue: 2
  • Publication Date: 2014
  • Doi Number: 10.1007/s10623-014-9942-8
  • Journal Name: DESIGNS CODES AND CRYPTOGRAPHY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.457-468
  • Middle East Technical University Affiliated: Yes

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.