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Computational and Algorithmic Problems in Finite Fields: Mathematics and its Applications, cartea 88

Autor Igor Shparlinski
en Limba Engleză Paperback – 29 oct 2012

Din seria Mathematics and its Applications

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Specificații

ISBN-13: 9789401047968
ISBN-10: 9401047960
Pagini: 256
Ilustrații: XII, 240 p.
Dimensiuni: 160 x 240 x 13 mm
Greutate: 0.36 kg
Ediția:1992
Editura: SPRINGER NETHERLANDS
Colecția Springer
Seria Mathematics and its Applications

Locul publicării:Dordrecht, Netherlands

Public țintă

Research

Cuprins

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.