TY - GEN

T1 - Classification of all the minimal bilinear algorithms for computing the coefficients of the product of two polynomials modulo a polynomial

AU - Averbuch, Amir

AU - Winograd, Shmuel

AU - Galil, Zvi

N1 - Publisher Copyright:
© 1986, Springer-Verlag.

PY - 1986

Y1 - 1986

N2 - In view of the results of Theorems III.1 and Theorem III.2, all the minimal bilinear algorithms for computing the coefficients of R(u)S(u) mod Q(u)l have multiplications of the form R(αj)S(αj) hence the algorithm requires large coefficients (as in l=1). Therefore using the identity R(u)S(u)=R(u)S(u) mod P(u) where degP(u)=2n − 1 with distinct irreducible, but not necessarily only linear, factors, does not reduce the large coefficients generated by the algorithm. In order to achieve better "practical" algorithms, non-minimal algorithms should be studied. In addition, classification of all the minimal algorithms for computing the coefficients of R(u)S(u) mod Q(u)l remains open.

AB - In view of the results of Theorems III.1 and Theorem III.2, all the minimal bilinear algorithms for computing the coefficients of R(u)S(u) mod Q(u)l have multiplications of the form R(αj)S(αj) hence the algorithm requires large coefficients (as in l=1). Therefore using the identity R(u)S(u)=R(u)S(u) mod P(u) where degP(u)=2n − 1 with distinct irreducible, but not necessarily only linear, factors, does not reduce the large coefficients generated by the algorithm. In order to achieve better "practical" algorithms, non-minimal algorithms should be studied. In addition, classification of all the minimal algorithms for computing the coefficients of R(u)S(u) mod Q(u)l remains open.

UR - http://www.scopus.com/inward/record.url?scp=85034640905&partnerID=8YFLogxK

U2 - 10.1007/3-540-16761-7_52

DO - 10.1007/3-540-16761-7_52

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AN - SCOPUS:85034640905

SN - 9783540167617

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 31

EP - 39

BT - Automata, Languages and Programming - 13th International Colloquium, Proceedings

A2 - Kott, Laurent

PB - Springer Verlag

T2 - 13th International Colloquium on Automata, Languages and Programming, ICALP 1986

Y2 - 15 July 1986 through 19 July 1986

ER -