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＜E-Book＞
Computational and Algorithmic Problems in Finite Fields / by Igor Shparlinski
(Mathematics and its Applications, Soviet Series ; 88)

Edition	1st ed. 1992.
Publisher	(Dordrecht : Springer Netherlands : Imprint: Springer)
Year	1992
Language	English
Size	XII, 240 p : online resource
Authors	*Shparlinski, Igor author SpringerLink (Online service)
Subjects	LCSH:Algebraic fields LCSH:Polynomials LCSH:Computer science -- Mathematics  All Subject Search LCSH:Computer science FREE:Field Theory and Polynomials FREE:Symbolic and Algebraic Manipulation FREE:Theory of Computation
Notes	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 HTTP:URL=https://doi.org/10.1007/978-94-011-1806-4

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