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Computational and algorithmic problems in finite fields

Computational and algorithmic problems in finite fields (Loan 2 times)

Material type
단행본
Personal Author
Shparlinski, Igor E.
Title Statement
Computational and algorithmic problems in finite fields / by Igor E. Shparlinski.
Publication, Distribution, etc
Dordrecht ;   Boston :   Kluwer Academic,   c1992.  
Physical Medium
xii, 240 p. : ill. ; 25 cm.
Series Statement
Mathematics and its applications. Soviet series ;v. 88.
ISBN
0792320573
Bibliography, Etc. Note
Includes bibliography(p. 191-237) and index.
Subject Added Entry-Topical Term
Finite fields (Algebra). Algebraic number theory.
000 00907camuuu200253 a 4500
001 000000903302
005 19990111162016.0
008 921005s1992 ne a b 001 0 eng
010 ▼a 92033537
020 ▼a 0792320573
040 ▼a DLC ▼c DLC ▼d DLC ▼d 244002
049 0 ▼l 151002405
050 0 0 ▼a QA247.3 ▼b .S475 1992
082 0 0 ▼a 512/.74 ▼2 20
090 ▼a 512.74 ▼b S559c
100 1 ▼a Shparlinski, Igor E.
245 1 0 ▼a Computational and algorithmic problems in finite fields / ▼c by Igor E. Shparlinski.
260 ▼a Dordrecht ; ▼a Boston : ▼b Kluwer Academic, ▼c c1992.
300 ▼a xii, 240 p. : ▼b ill. ; ▼c 25 cm.
490 1 ▼a Mathematics and its applications. Soviet series ; ▼v v. 88.
504 ▼a Includes bibliography(p. 191-237) and index.
650 0 ▼a Finite fields (Algebra).
650 0 ▼a Algebraic number theory.
830 0 ▼a Mathematics and its applications (Kluwer Academic Publishers). ▼p Soviet series ; ▼v 88.

Holdings Information

No. Location Call Number Accession No. Availability Due Date Make a Reservation Service
No. 1 Location Sejong Academic Information Center/Science & Technology/ Call Number 512.74 S559c Accession No. 151002405 Availability Available Due Date Make a Reservation Service B M

Contents information

Table of Contents


CONTENTS
Series Editor's Preface ⅸ
Preface = ⅹ
Acknowledgements = xi
Notations = ⅸ
Introduction = 1
Chapter 1. Polynomial Factorization = 7
 1. Univariate factorization = 7
 2. Multivariate factorization = 16
 3. Other polynomial decompositions = 20
Chapter 2. Finding irreducible and primitive polyziginials = 21
 1. Construction of irreducible polynomials = 21
 2. Construction of primitive polynomials = 27
Chapter 3. The distribution of irreducible and priniitive polynomials = 30
 1. Distribution of irreducible and primitive polynomials = 30
 2. Irreducible and primitive polynomials of a given height and weight = 42
 3. Sparse polynomials = 46
 4. Applications to algebraic number fields = 47
Chapter 4. Bases and computation in finite fields = 49
 1. Construction of some special bases for finite fields = 49
 2. Discrete logarithm and Zech's logarithm = 54
 3. Polynomial multiplication and multiplicative complexity infinite fields = 56
 4. Other algorithms in finite fields = 64
Chapter 5. Coding theory and algebraic curves = 72
 1. Codes and points on algebraic curves = 72
 2. Codes and exponential sums = 86
 3. Codes and lattice packings and coverings = 92
Chapter 6. Elliptic curves = 99
 1. Some general properties = 99
 2. Distribution of primitive points on elliptic curves = 105
Chapter 7. Recurrent sequences in finite fields and leylic lineir codes = 109
 1. Distribution of values of recurrent sequences = 109
 2. Applications of recurrent sequences = 113
 3. Cyclic codes and recurrent sequences = 116
Chapter 8. Finite fields and discrete mathematics = 122
 1. Cryptography and permutation polynomials = 122
 2. Graph theory, combinatorics, Boolean functions = 129
 3. Enumeration problems in finite fields = 136
Chapter 9. Congruences = 139
 1. Optimal coefficients and pseudo-random numbers = 139
 2. Residues of exponential functions = 143
 3. Modular arithmetic = 148
 4. Other applications = 150
Chapter 10. Some related problems = 153
 1. Integer factorization, primality testing and the greatest common divisor = 153
 2. Computational algebraic number theory = 155
 3. Algebraic complexity theory = 156
 4. Polynomials with integer coefficients = 159
Appendix 1 = 161
Appendix 2 = 164
Appendix 3 = 165
Addendum = 166
References = 191
Index = 238


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