Modeling finite fields with mathematica

Applications to the computation of exponential sums and to the solution of equations over finite fields
  • Antonio Vantaggiato
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 722)


This paper proposes an implementation model for finite fields GF[mq], m prime, based on a hybrid architecture that integrates symbolic programming developed in Mathematica with an imperative C language module. Its aim is to enable the user to write algorithms to perform calculations in GF's by using Mathematica's programming language and built-in math functions. First, the system's architecture is presented and it is shown that the proposed model has linear time complexity (O(q)) for all algebraic operations. Finally, we show the developed modules for the computation of exponential sums and the solution of equations over finite fields.


Finite Field Hybrid Architecture Field Element Abstract Data Type Sacred Heart 
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  1. 1.
    A. Cáceres, O. Moreno: On the Estimation of Minimum Distance of Duals of BCH Codes. Congressus Numerantium 81, (1991).Google Scholar
  2. 2.
    J.H. Davenport: Current Problems in Computer Algebra Systems Design. In: A. Miola (ed.): Design and Implementation of Symbolic Computation Systems (DISCO '90). Berlin: Springer-Verlag 1990.Google Scholar
  3. 3.
    R. Lidl, H. Niederreiter. Finite Fields. In: G.C. Rota (ed): Encyclopedia of Mathematics and its Applications. Cambridge: Cambridge University Press 1984.Google Scholar
  4. 4.
    R. Maeder. Abstract Data Types. Tutorial Notes, Mathematica Conference, Boston. Wolfram Research 1992.Google Scholar
  5. 5.
    Wolfram Research, Inc. MathLink Reference Guide. Champain, Ill. 1992.Google Scholar
  6. 6.
    C. Moreno, O. Moreno. Exponential Sums and Goppa Codes I, Proc. of the American Mathematical Society, Vol. 3, No. 2, (Feb. 1991).Google Scholar
  7. 7.
    S. Wolfram. Mathematica. Reading, Mass.: Addison-Wesley 1992.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Antonio Vantaggiato
    • 1
  1. 1.Computer Science ProgramUniversity of the Sacred HeartSan JuanPuerto Rico

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