An improvement of the construction of the D.V. and G.V. Chudnovsky algorithm for multiplication in finite fields

Theoretical Computer Science

Volumn 352, Issue 1-3, 2006, Pages 293-305

  Ballet, S ^a  

^a Polynésie Française   (France)

Author keywords

Algebraic curves; Algebraic function fields; Algorithm; Bilinear complexity; Finite fields

Indexed keywords

ALGEBRAIC CURVES; ALGEBRAIC FUNCTION FIELDS; BILINEAR COMPLEXITY; FINITE FIELDS;

ALGORITHMS; INTERPOLATION;

COMPUTER SCIENCE;

EID: 32644454131     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2005.11.045     Document Type: Article

References (19)

1. q Finite Fields Their Appl. 5 1999 364 377
2. 16 of degree 13, 14, and 15 J. Pure Appl. Algebra 171 2002 149 164
3. q Finite Fields Their Appl. 9 2003 472 478
4. S. Ballet, and R. Rolland Multiplication algorithm in a finite field and tensor rank of the multiplication J. Algebra 272/1 2004 173 185
5. S. Ballet, and J. Chaumine On the bounds of the bilinear complexity of multiplication in some finite fields Appl. Algebra Eng. Comm. Comput. 15 2004 205 211
6. q, J. Number Theory, to appear.
7. S. Ballet, D. Le Brigand, R. Rolland, The definition field of a tower of function fields and applications, in: Proceedings AGCT-10 (2005), accepted.
8. 4 Appl. Algebra Eng. Comm. Comput. 2 1991 15 20
9. J. Chaumine, Corps de fonctions algébriques et algorithme de D.V. Chudnovsky and G.V. Chudnovsky pour la multiplication dans les corps finis, Thèse de doctorat, April 2005.
10. J. Chaumine, On the bilinear complexity of the multiplication in small finite fields, submitted for publication.
11. D.V. Chudnovsky, and G.V. Chudnovsky Algebraic complexities and algebraic curves over finite fields J. Complexity 4 1988 285 316
12. H.F. De Groote Characterization of division algebras of minimal rank and the structure of their algorithm varieties SIAM J. Comput. 12 1 1983 101 117
13. M. Deuring, Lectures on the Theory of Algebraic Functions of One Variable, Lectures Notes in Mathematics, Vol. 314. Springer, Heidelberg, New York, Tokyo, 1973.
14. A. Garcia, and H. Stichtenoth A tower of Artin-Schreier extensions of function fields attaining the Drinfeld-Vladut bound Invent. Math. 121 1995 211 222
15. A. Garcia, H. Stichtenoth, and H.-G. Ruck On tame towers over finite fields J. die reine und angewandte Mathematik 557 2003 53 80
16. A. Lidl, and H. Niederreiter Finite Fields, Encyclopedia of Mathematics and its Applications Vol. 20 1983 Addison-Wesley Reading, MA
17. M.A. Shokrollahi Optimal algorithms for multiplication in certain finite fields using algebraic curves SIAM J. Comput. 21 6 1992 1193 1198
18. I.E. Shparlinski, M.A. Tsfasman, S.G. Vladut, Curves with Many Points and Multiplication in Finite Fields, Lectures Notes in Mathematics, Vol. 1518, Springer, Berlin, 1992, pp. 145-169.
19. S. Winograd On multiplication in algebraic extension fields Theoret. Comput. Sci. 8 1979 359 377