Contents

• 1. Introduction
• 2. Finite Fields
  • 2.1 Characteristic
  • 2.2 Order and degree of an element
  • 2.3 Primitive elements
  • 2.4 Descriptions of a given finite field
  • 2.5 Frobenius automorphism
  • 2.6 Subfields and subgroups
  • 2.7 Trace of an element
  • 2.8 Discrete logarithm and Zech logarithm
• 3. as example
  • 3.1 Vector space structure of
  • 3.2 Zech's logarithms in
  • 3.3 Using the Zech table to solve quadratic equations
• 4. Huber's paper revisited : the group
  • 4.1 Some mappings
  • 4.2 Elementary properties or Zech logarithms
  • 4.3 Cosets and coset mappings
  • 4.4 Frobenius cycles
  • 4.5 Fibonacci cycles
  • 4.6 Flip-flop cycles
  • 4.7 The dimension of the group
  • 4.8 The hidden polyhedrons
• 5. Effective computation of
  • 5.1 Straightforward calculation for Zech's tables
  • 5.2 Finding irreducible or primitive polynomials
  • 5.3 Admissible exponents
  • 5.4 Rebuilding from an admissible exponent
  • 5.5 A probabilistic method
• 6. Efficient exponents
  • 6.1 Random exploration
  • 6.2 Improving efficiency
  • 6.3 Further values
• 7. Discussion
• Bibliography
• Contents

Figure 5: A5_walk

Figure 6: wheel

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