Abstract
It is shown that computing the coefficients of the product of two degree-n polynomials over a q-element field by means of a quadratic algorithm requires at least \((3+ \frac{(q-1)^2}{q^5+(q-1)^3})n-o(n)\) multiplications, whereas the best lower bound known from the literature is 3n – o(n).
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Kaminski, M. (2005). A Lower Bound on the Complexity of Polynomial Multiplication Over Finite Fields. In: Diekert, V., Durand, B. (eds) STACS 2005. STACS 2005. Lecture Notes in Computer Science, vol 3404. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31856-9_40
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DOI: https://doi.org/10.1007/978-3-540-31856-9_40
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