Geodesic
Implementing the multiplication of polynomial matrices over the field $GF(2)$ by means of the fast Fourier transform
Diskretnaya Matematika, Tome 25 (2013) no. 1, pp. 111-120.

Voir la notice de l'article provenant de la source Math-Net.Ru

@article{DM_2013_25_1_a6,
     author = {A. S. Ryzhov},
     title = {Implementing the multiplication of polynomial matrices over the field $GF(2)$ by means of the fast {Fourier} transform},
     journal = {Diskretnaya Matematika},
     pages = {111--120},
     publisher = {mathdoc},
     volume = {25},
     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2013_25_1_a6/}
}
TY  - JOUR
AU  - A. S. Ryzhov
TI  - Implementing the multiplication of polynomial matrices over the field $GF(2)$ by means of the fast Fourier transform
JO  - Diskretnaya Matematika
PY  - 2013
SP  - 111
EP  - 120
VL  - 25
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2013_25_1_a6/
LA  - ru
ID  - DM_2013_25_1_a6
ER  - 
%0 Journal Article
%A A. S. Ryzhov
%T Implementing the multiplication of polynomial matrices over the field $GF(2)$ by means of the fast Fourier transform
%J Diskretnaya Matematika
%D 2013
%P 111-120
%V 25
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2013_25_1_a6/
%G ru
%F DM_2013_25_1_a6
A. S. Ryzhov. Implementing the multiplication of polynomial matrices over the field $GF(2)$ by means of the fast Fourier transform. Diskretnaya Matematika, Tome 25 (2013) no. 1, pp. 111-120. http://geodesic.mathdoc.fr/item/DM_2013_25_1_a6/

[1] Thomé E., “Subquadratic computation of vector generating polynomials and improvement of the block Wiedemann algorithm”, J. Symb. Comput., 33 (2002), 757–775 | DOI | MR | Zbl

[2] Coppersmith D., “Solving linear equations over $GF(2)$ via block Wiedemann algorithm”, Math. Comput., 62:205 (1994), 333–350 | MR | Zbl

[3] Kleinjung T., Aoki K., Franke J., Lenstra A. K., Thomé E., Bos J. W., Gaudry P., Kruppa A., Montgomery P. L., Osvik D. A., te Riele H., Timofeev A., Zimmermann P., “Factorization of a 768-bit RSA modulus”, Lecture Notes Comput. Sci., 6223, ed. Rabin T., 2010, 333–350 | DOI | MR | Zbl

[4] Karatsuba A. A., “Slozhnost vychislenii”, Trudy Matematicheskogo instituta im. V. A. Steklova RAN, 211, 1995, 186–202 | MR | Zbl

[5] Schönhage A., Strassen V., “Schnelle Multiplikation grosser Zahlen”, Computing, 7 (1971), 281–292 | DOI | MR

[6] Burgisser P., Clausen A., Shokrollahi A., Algebraic complexity theory, Springer, Berlin, 1997 | MR

[7] Furer M., “Faster integer multiplication”, Proc. STOC' 2007, ACM, New York, 2007, 57–66 | MR

[8] Knut D. E., Iskusstvo programmirovaniya: Poluchislennye metody, v. 2, Vilyams, Moskva, 2007

[9] Pollard J. M., “The fast Fourier transform in a finite field”, Math. Comput., 25, 365–374 | MR | Zbl

[10] Schönhage A., “Schnelle Multiplikation von Polynomen über Körpern der Charakteristik 2”, Acta Inf., 7 (1977), 395–398 | DOI | MR