Efficient dot product over word-size finite fields

We want to achieve efficiency for the exact computation of the dot product of two vectors over word size finite fields. We therefore compare the practical behaviors of a wide range of implementation techniques using different representations. The techniques used include floating point representations, discrete logarithms, tabulations, Montgomery reduction, delayed modulus. Our implementations have many symbolic linear algebra applications: matrix multiplication, symbolic triangularization, system solving, exact determinant computation, matrix normal form are such examples.

• Type: Journal
• Year: 2004
• Where: CORR
• Authors: Jean-Guillaume Dumas
• Keywords: CORR 2004, Education, Exact Computation, Exact Determinant Computation, Symbolic Linear Algebra