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Classification of all the minimal bilinear algorithms for computing the coefficients of the product of two polynomials modulo a polynomial

  • Amir Averbuch
  • Shmuel Winograd
  • Zvi Galil
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 226)

Abstract

In view of the results of Theorems III.1 and Theorem III.2, all the minimal bilinear algorithms for computing the coefficients of R(u)S(u) mod Q(u) l have multiplications of the form R(αj)S(αj) hence the algorithm requires large coefficients (as in l=1). Therefore using the identity R(u)S(u)=R(u)S(u) mod P(u) where degP(u)=2n − 1 with distinct irreducible, but not necessarily only linear, factors, does not reduce the large coefficients generated by the algorithm. In order to achieve better "practical" algorithms, non-minimal algorithms should be studied. In addition, classification of all the minimal algorithms for computing the coefficients of R(u)S(u) mod Q(u) l remains open.

Keywords

Bilinear Form Discrete Fourier Transform Bilinear Mapping Minimal Algorithm Zero Divisor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Amir Averbuch
    • 1
  • Shmuel Winograd
    • 1
  • Zvi Galil
    • 2
    • 3
  1. 1.IBM T.J. Watson Research CenterYorktown Heights
  2. 2.Dept. of Computer ScienceColumbia UniversityNew York
  3. 3.Tel-Aviv UniversityIsrael

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