On the tensor rank of multiplication in any extension of F2

Journal of Complexity

Volumn 27, Issue 2, 2011, Pages 230-245

  Ballet, Stéphane ^a,b   Pieltant, Julia ^a,b  

^a AIX MARSEILLE UNIVERSITÉ   (France)

^b ERISCS Groupe de Recherche Informatique des Systèmes Communicants Sécurisés   (France)

Author keywords

Algebraic function fields; Algorithm; Finite fields; Tensor rank; Tower of function fields

Indexed keywords

ALGORITHMS; FINITE ELEMENT METHOD; FUNCTIONS;

ALGEBRAIC FUNCTION FIELD; ASYMPTOTIC BOUNDS; DERIVATIVE EVALUATION; FINITE FIELDS; FUNCTION FIELDS; GENERALIZED ALGORITHMS; TENSOR RANKS;

TENSORS;

EID: 79952449866     PISSN: 0885064X     EISSN: 10902708     Source Type: Journal    
DOI: 10.1016/j.jco.2011.01.008     Document Type: Article

References (22)

1. Nicolas Arnaud, valuations drives, multiplication dans les corps finis et codes correcteurs, Ph.D. Thesis, Universit de la Mditerrane, Institut de Mathmatiques de Luminy, 2006.
2. Stphane Ballet Curves with many points and multiplication complexity in any extension of Fq Finite Fields and their Applications 5 1999 364 377
3. Stphane Ballet Low increasing tower of algebraic function fields and bilinear complexity of multiplication in any extension of Fq Finite Fields and their Applications 9 2003 472 478
4. Stphane Ballet On the tensor rank of the multiplication in the finite fields Journal of Number Theory 128 2008 1795 1806
5. Stphane Ballet, and Jean Chaumine On the bounds of the bilinear complexity of multiplication in some finite fields Applicable Algebra in Engineering, Communication and Computing 15 2004 205 211
6. Stphane Ballet, and Dominique Le Brigand On the existence of non-special divisors of degree g and g - 1 in algebraic function fields over Fq Journal of Number Theory 116 2006 293 310 (Pubitemid 43137891)
7. Stphane Ballet, Dominique Le Brigand, Robert Rolland, On an application of the definition field descent of a tower of function fields, in: Proceedings of the Conference Arithmetic, Geometry and Coding Theory, AGCT 2005, vol. 21, Socit Mathmatique de France, sr. Sminaires et Congrs, 2009, pp. 187203.
8. Stphane Ballet, Christophe Ritzenthaler, and Robert Rolland On the existence of dimension zero divisors in algebraic function fields defined over Fq Acta Arithmetica 143 4 2010 377 392
9. Stphane Ballet, and Robert Rolland Families of curves over any finite field attaining the generalized DrinfeldVladut bound Publ. Math. Univ. Franche-Comt Besanon Algbr. Theor. Nr. 2011 5 18
10. Stphane Ballet, and Robert Rolland Multiplication algorithm in a finite field and tensor rank of the multiplication Journal of Algebra 272 1 2004 173 185 (Pubitemid 38131033)
11. Ulrich Baum, and Amin Shokrollahi An optimal algorithm for multiplication in F 256 F 4 Applicable Algebra in Engineering, Communication and Computing 2 1 1991 15 20
12. Peter Bürgisser, Michael Clausen, and Amin Shokrollahi Algebraic Complexity Theory Grundlehren der Mathematischen Wissenchaften vol. 315 1997 Springer
13. Murat Cenk, and Ferruh zbudak On multiplication in finite fields Journal of Complexity 2009 10.1016/j.jco.2009.11.002
14. David Chudnovsky, and Gregory Chudnovsky Algebraic complexities and algebraic curves over finite fields Journal of Complexity 4 1988 285 316
15. Mario Daberkow, Claus Fieker, Jürgen Klüners, Michael E. Pohst, Roegner Katherine, and Klaus Wildanger KANT V4 Journal of Symbolic Computation 24 1997 267 283 (Pubitemid 127167875)
16. Hans de Groote Characterization of division algebras of minimal rank and the structure of their algorithm varieties SIAM Journal on Computing 12 1 1983 101 117
17. Arnaldo Garcia, and Henning Stichtenoth A tower of ArtinSchreier extensions of function fields attaining the DrinfeldVladut bound Inventiones Mathematicae 121 1995 211 222
18. Harald Niederreiter, and Chaoping Xing Algebraic Geometry in Coding Theory & Cryptography 2009 Princeton University Press
19. Amin Shokhrollahi Optimal algorithms for multiplication in certain finite fields using algebraic curves SIAM Journal on Computing 21 6 1992 1193 1198
20. Igor Shparlinski, Michael Tsfasman, and Serguei Vladut Curves with many points and multiplication in finite fields H. Stichtenoth, M.A. Tsfasman, Coding Theory and Algebraic Geometry Lectures Notes in Mathematics vol. 1518 1992 Springer-Verlag Berlin 145 169 Proceedings of AGCT-3 Conference, June 1721, 1991, Luminy
21. Henning Stichtenoth Algebraic Function Fields and Codes second ed. Graduate Texts in Mathematics vol. 254 2008 Springer
22. Shmuel Winograd On multiplication in algebraic extension fields Theoretical Computer Science 8 1979 359 377