Finite Fields and Applications: Proceedings of the Third International Conference, Glasgow, July 1995

ISBN-13: 9780521567367 / Angielski / Miękka / 1996 / 424 str.

Stephen D. Cohen; Harald Niederreiter; S. Cohen

Opis

Finite fields are algebraic structures in which there is much research interest. This book gives a state-of-the-art account of finite fields and their applications in communications (coding theory, cryptology), combinatorics, design theory, quasirandom points, algorithms and their complexity. Typically, theory and application are tightly interwoven in the survey articles and original research papers included here. The book also demonstrates interconnections with other branches of pure mathematics such as number theory, group theory and algebraic geometry. This volume is an invaluable resource for any researcher in finite fields or related areas.

Recenzje

'… a state-of-the-art account of the area of finite fields and their applications.' L'Enseignement Mathématique

Spis treści

1. Factorizations over finite fields Abhyankar; 2. Class number in totally imaginary extensions Aubry; 3. Automorphism groups and permutation groups Berger; 4. A construction of bent functions Carlet; 5. Monodromy groups of classical families Cohen and Matthews; 6. Wan's bound Cusick and Müller; 7. Factorization; 8. Algorithms Fleischmann and Roelse; 9. Minimal polynomials for certain Gauss periods Gurak; 10. Completely free elements Hachenberger; 11. Exponential sums over Galois rings Helleseth et al.; 12. Mutually orthogonal Latin squares Jungnickel; 13. Examples of small hybrid sums Lahtonen; 14. Cellular automata Lange; 15. A new class of two weight code Langevin et al; 16. Construction of digital (t,m,s)-nets Lawrence et al; 17. A family of exceptional polynomials Lenstra and Zieve; 18. Estimates of character sums Li; 19. Carmichael-Carlitz polynomials Mauduit; 20. Open problems and conjectures Mullen and Shparlinski; 21. Quasirandom points Niederreiter and Xing; 22. Character sets to decode cyclic codes Rong and Helleseth; 23. Approximate constructions in finite fields Shparlinski; 24. Periodicity properties of linear recurrences Somer; 25. Factoring cyclotomic polynomials Stein; 26. Character sums and coding theory Stepanov; 27. L-functions of algebraic varieties Wan; 28. Generalizations of R'edei functions Young.