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Complete Mapping Polynomials over Finite Field F16

  • Yuan Yuan
  • Yan Tong
  • Huanguo Zhang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4547)

Abstract

A polynomial f(x) over F q , the finite field with q elements, is called a complete mapping polynomial if the two mappings F q F q respectively defined by f(x) and f(x) + x are one-to-one. In this correspondence, complete mapping polynomials over F 16 are considered. The nonexistence of the complete mapping polynomial of degree 9 and the existence of the ones of degree 8 and 11 are proved; the result that the reduced degree of complete mapping polynomials over F 16 are 1, 4, 8, 10, 11, 12, 13 is presented; and by searching with computer, the degree distribution of complete mapping polynomials over the field is given.

Keywords

permutation polynomials complete mapping polynomials unique factorization domain 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Yuan Yuan
    • 1
  • Yan Tong
    • 1
  • Huanguo Zhang
    • 1
  1. 1.School of Computer, Wuhan University, Wuhan, Hubei, 430072China

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