Computational and Algorithmic Problems in Finite Fields
Main Author: | |
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Format: | eBook |
Language: | English |
Published: |
Dordrecht
Springer Netherlands
1992, 1992
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Edition: | 1st ed. 1992 |
Series: | Mathematics and its Applications, Soviet Series
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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