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On the Bounds of the Bilinear Complexity of Multiplication in Some Finite Fields

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Abstract.

From the existence of a tower of algebraic function fields, we improve upper bounds on the bilinear complexity of multiplication in all the extensions of the finite fields and where p is a prime ≥5. In particular, we improve asymptotic upper bounds on this complexity for prime finite fields of characteristic p>5.

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Authors and Affiliations

  1. Laboratoire de Géométrie Algébrique et Applications à la Théorie de l’Information, Université de la Polynésie Française, B.P. 6570, 98702 Faa’a, Tahiti, Polynésie Française

    Stéphane Ballet & Jean Chaumine

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  1. Stéphane Ballet
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  2. Jean Chaumine
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Correspondence to Stéphane Ballet.

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Ballet, S., Chaumine, J. On the Bounds of the Bilinear Complexity of Multiplication in Some Finite Fields. AAECC 15, 205–221 (2004). https://doi.org/10.1007/s00200-004-0155-7

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  • DOI: https://doi.org/10.1007/s00200-004-0155-7

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