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- The paper is concerned with the implementation of the fast multiplication of binary polynomials and polynomial matrices on 64-bit computers. A method is proposed for an efficient implementation of the fast Fourier transform with the use of the addition and multiplication operations modulo 2 64  subject to a bound on the size of the problem. Comparative performance results are given showing substantial advantages of the implementation of the algorithm proposed over the function of multiplication of binary polynomials from the NTL mathematical library for multiplication of polynomials of degree exceeding 2 25  and multiplication of square polynomial matrices of degree at least 2 14  and of size at least 32 × 32.

Implementing the multiplication of polynomial matrices over the field GF(2) by means of the fast Fourier transform