### Multiplicative complexity of polynomial multiplication over finite fieldsMultiplicative complexity of polynomial multiplication over finite fields

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 Author Kaminski, Michael ♦ Bshouty, Nader H. Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©1989 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Abstract Let $\textit{M}q(\textit{n})$ denote the number of multiplications required to compute the coefficients of the product of two polynomials of degree $\textit{n}$ over a $\textit{q}-element$ field by means of bilinear algorithms. It is shown that $\textit{Mq}(\textit{n})$ ≱ $3\textit{n}$ - $\textit{o}(\textit{n}).$ In particular, if $\textit{q}/2$ < $\textit{n}$ ⪇ $\textit{q}$ + 1, we establish the tight bound $\textit{Mq}(\textit{n})$ = $3\textit{n}$ + 1 $[\textit{q}/2].The$ technique we use can be applied to analysis of algorithms for multiplication of polynomials modulo a polynomial as well. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 1989-01-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 36 Issue Number 1 Page Count 21 Starting Page 150 Ending Page 170

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Source: ACM Digital Library