Computational and Algorithmic Problems in Finite Fields

Bibliographic Details
Main Author: Shparlinski, Igor
Format: eBook
Language:English
Published: Dordrecht Springer Netherlands 1992, 1992
Edition:1st ed. 1992
Series:Mathematics and its Applications, Soviet Series
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 1. Polynomial Factorization
  • 1. Univariate factorization
  • 2. Multivariate factorization
  • 3. Other polynomial decompositions
  • 2. Finding irreducible and primitive polynomials
  • 1. Construction of irreducible polynomials
  • 2. Construction of primitive polynomials
  • 3. The distribution of irreducible and primitive polynomials
  • 1. Distribution of irreducible and primitive polynomials
  • 2. Irreducible and primitive polynomials of a given height and weight
  • 3. Sparse polynomials
  • 4. Applications to algebraic number fields
  • 4. Bases and computation in finite fields
  • 1. Construction of some special bases for finite fields
  • 2. Discrete logarithm and Zech’s logarithm
  • 3. Polynomial multiplication and multiplicative complexity in finite fields
  • 4. Other algorithms in finite fields
  • 5. Coding theory and algebraic curves
  • 1. Codes and points on algebraic curves
  • 2. Codes and exponential sums
  • 3. Codes and lattice packings and coverings
  • 6. Elliptic curves
  • 1. Some general properties
  • 2. Distribution of primitive points on elliptic curves
  • 7. Recurrent sequences in finite fields and leyelic linear codes
  • 1. Distribution of values of recurrent sequences
  • 2. Applications of recurrent sequences
  • 3. Cyclic codes and recurrent sequences
  • 8. Finite fields and discrete mathematics
  • 1. Cryptography and permutation polynomials
  • 2. Graph theory, combinatorics, Boolean functions
  • 3. Enumeration problems in finite fields
  • 9. Congruences
  • 1. Optimal coefficients and pseudo-random numbers
  • 2. Residues of exponential functions
  • 3. Modular arithmetic
  • 4. Other applications
  • 10. Some related problems
  • 1. Integer factorization, primality testing and the greatest common divisor
  • 2. Computational algebraic number theory
  • 3. Algebraic complexity theory
  • 4.Polynomials with integer coefficients
  • Appendix 1
  • Appendix 2
  • Appendix 3
  • Addendum
  • References