Computational and algorithmic problems in finite fields /
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| Author / Creator: | Shparlinski, Igor E. |
|---|---|
| Imprint: | Dordrecht ; Boston : Kluwer Academic, c1992. |
| Description: | xii, 240 p. : ill. ; 25 cm. |
| Language: | English |
| Series: | Mathematics and its applications. Soviet series ; v. 88 Mathematics and its applications (Kluwer Academic Publishers). Soviet series 88. |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/1473304 |
Table of Contents:
- Ch. 1. Polynomial Factorization. 1. Univariate factorization. 2. Multivariate factorization. 3. Other polynomial decompositions
- Ch. 2. Finding irreducible and primitive polynomials. l. Construction of irreducible polynomials. 2. Construction of primitive polynomials
- Ch. 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
- Ch. 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
- Ch. 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
- Ch. 6. Elliptic curves. 1. Some general properties. 2. Distribution of primitive points on elliptic curves
- Ch. 7. Recurrent sequences in finite fields and cyclic linear codes. 1. Distribution of values of recurrent sequences. 2. Applications of recurrent sequences. 3. Cyclic codes and recurrent sequences
- Ch. 8. Finite fields and discrete mathematics. 1. Cryptography and permutation polynomials. 2. Graph theory, combinatorics, Boolean functions. 3. Enumeration problems in finite fields
- Ch. 9. Congruences. 1. Optimal coefficients and pseudo-random numbers. 2. Residues of exponential functions. 3. Modular arithmetic. 4. Other applications
- Ch. 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.
