, Curves with many points and multiplication complexity in any extension of Fq. Finite Fields and Their Applications, pp.364-377, 1999.
, Low increasing tower of algebraic function fields and bilinear complexity of multiplication in any extension of Fq. Finite Fields and Their Applications, pp.472-478, 2003.
, On the tensor rank of the multiplication in the finite fields, Journal of Number Theory, vol.128, issue.6, pp.1795-1806, 2008.
DOI : 10.1016/j.jnt.2007.06.010
URL : https://hal.archives-ouvertes.fr/hal-01079416
, On the Bounds of the Bilinear Complexity of Multiplication in Some Finite Fields, Applicable Algebra in Engineering, Communication and Computing, vol.8, issue.3-4, pp.205-211, 2004.
DOI : 10.1007/s00200-004-0155-7
, On the existence of non-special divisors of degree g and <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi>g</mml:mi><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:math> in algebraic function fields over <mml:math altimg="si2.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">F</mml:mi></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:msub></mml:math>, Journal of Number Theory, vol.116, issue.2, pp.293-310, 2006.
DOI : 10.1016/j.jnt.2005.04.009
, On an application of the definition field descent of a tower of function fields, Proceedings of the Conference Arithmetic, Geometry and Coding Theory, pp.187-203, 2005.
URL : https://hal.archives-ouvertes.fr/hal-01086197
, On the tensor rank of multiplication in any extension of <mml:math altimg="si1.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">F</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math>, Journal of Complexity, vol.27, issue.2, pp.230-245, 2011.
DOI : 10.1016/j.jco.2011.01.008
, Multiplication algorithm in a finite field and tensor rank of the multiplication, Journal of Algebra, vol.272, issue.1, pp.173-185, 2004.
DOI : 10.1016/j.jalgebra.2003.09.031
, Families of curves over any finite field attaining the generalized Drinfeld-Vladut bound, Publ. Math. Univ. Franche-Comté Besançon Algèbr. Theor. Nr, pp.5-18, 2011.
URL : https://hal.archives-ouvertes.fr/hal-01079406
, An optimal algorithm for multiplication in F256/F4, Applicable Algebra in Engineering, Communication and Computing, pp.15-20, 1991.
DOI : 10.1007/BF01810851
, Asymptotic Bound for Multiplication Complexity in the Extensions of Small Finite Fields, IEEE Transactions on Information Theory, vol.58, issue.7, pp.4930-4935, 2012.
DOI : 10.1109/TIT.2011.2180696
, On multiplication in finite fields, Journal of Complexity, vol.26, issue.2, pp.172-186, 2010.
DOI : 10.1016/j.jco.2009.11.002
, Algebraic complexities and algebraic curves over finite fields, Journal of Complexity, vol.4, issue.4, pp.285-316, 1988.
DOI : 10.1016/0885-064X(88)90012-X
URL : https://www.ncbi.nlm.nih.gov/pmc/articles/PMC304516/pdf
, Characterization of division algebras of minimal rank and the structure of their algorithm varieties, SIAM Journal on Computing, vol.12, issue.1, pp.101-117, 1983.
, A tower of Artin-Schreier extensions of function fields attaining the Drinfeld-Vladut bound, Inventiones Mathematicae, vol.84, issue.No. 1, pp.211-222, 1995.
DOI : 10.1007/BF01884295
, On tame towers over finite fields, Journal fur die reine und angewandte Mathematik, pp.53-80, 2003.
DOI : 10.1515/crll.2003.034
, Bilinear complexity of algebras and the Chudnovsky???Chudnovsky interpolation method, Journal of Complexity, vol.28, issue.4, pp.489-517, 2012.
DOI : 10.1016/j.jco.2012.02.005
, Optimal Algorithms for Multiplication in Certain Finite Fields Using Elliptic Curves, SIAM Journal on Computing, vol.21, issue.6, pp.1193-1198, 1992.
DOI : 10.1137/0221071
, Curves with many points and multiplication in finite fields, Coding Theory and Algebraic Geometry, number 1518 in Lectures Notes in Mathematics Proceedings of AGCT-3 Conference, pp.145-169, 1991.
, On multiplication in algebraic extension fields, Theoretical Computer Science, vol.8, issue.3, pp.359-377, 1979.
DOI : 10.1016/0304-3975(79)90017-3
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