Implementing the multiplication of polynomial matrices over the field GF(2) by means of the fast Fourier transform
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A. S. Ryzhov
Abstract
- 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 264 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 225 and multiplication of square polynomial matrices of degree at least 214 and of size at least 32 × 32.
© 2013 by Walter de Gruyter GmbH & Co.
Articles in the same Issue
- Masthead
- On the solvability of the equational theory of commutative medial n-ary groupoids
- Estimating the stability radius of the vector MAX-CUT problem
- Statistical estimation of parameters for binary Markov chain models with embeddings
- A simplified proof of a lower complexity estimate
- Finite groups with nilpotent and Hall subgroups
- Implementing the multiplication of polynomial matrices over the field GF(2) by means of the fast Fourier transform
- The number of differences in groups of prime order
- Characteristic submodules of injective modules
- On transformations of probability distributions by read-once quasigroup formulae
Articles in the same Issue
- Masthead
- On the solvability of the equational theory of commutative medial n-ary groupoids
- Estimating the stability radius of the vector MAX-CUT problem
- Statistical estimation of parameters for binary Markov chain models with embeddings
- A simplified proof of a lower complexity estimate
- Finite groups with nilpotent and Hall subgroups
- Implementing the multiplication of polynomial matrices over the field GF(2) by means of the fast Fourier transform
- The number of differences in groups of prime order
- Characteristic submodules of injective modules
- On transformations of probability distributions by read-once quasigroup formulae
