Computational and algorithmic problems in finite fields
著者
書誌事項
Computational and algorithmic problems in finite fields
（Mathematics and its applications, . Soviet series ; 88）
Kluwer Academic, c1992
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注記
References: p. 191-237
Includes index
内容説明・目次
内容説明
This volume presents an exhaustive treatment of computation and algorithms for finite fields. Topics covered include polynomial factorization, finding irreducible and primitive polynomials, distribution of these primitive polynomials and of primitive points on elliptic curves, constructing bases of various types, and new applications of finite fields to other areas of mathematics. For completeness, also included are two special chapters on some recent advances and applications of the theory of congruences (optimal coefficients, congruential pseudo-random number generators, modular arithmetic etc.), and computational number theory (primality testing, factoring integers, computing in algebraic number theory, etc). The problems considered here have many applications in computer science, coding theory, cryptography, number theory and discrete mathematics. The level of discussion presupposes only a knowledge of the basic facts on finite fields, and the book can be recommended as supplementary graduate text. For researchers and students interested in computational and algorithmic problems in finite fields.
目次
- Polynomial factorization
- finding irreducible and primitive polynomials
- the distribution of irreducible and primitive polynomials
- bases and computation in finite fields
- coding theory and algebraic curves
- elliptic curves
- recurrent sequences in finite fields and linear cyclic codes
- finite fields and discrete mathematics
- congruences
- some related problems.
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