Multiplier is the major component for processing of large amount of data in DSP applications. Using different recoding schemes in Fused Add-Multiply (FAM) design for the reduction of power and look up tables. The performance of 16-bit signed and unsigned multipliers were designed and obtained results are tabulated using Efficient Modified Booth Recoding (EMBR) techniques, which can be used for ...

Figure 1 Webster Front Page 1634 ..................................................................................................................... 2 Figure 2 Webster's 1634 Compound Interest Table............................................................................................ 2 Figure 3 Frontispiece of Barreme, 1762 ..................................................................

We prove that, assuming GRH, there are only finitely many newforms with rational Fourier coefficients and complex multiplication for fixed weight up to twisting. We produce tables of such forms for weights 3 and 4, where this finiteness holds unconditionally. We also comment on geometric realizations.

The variety of quasigroups satisfying the identity (xy)(zy) = xz mirrors the variety of groups, and offers a new look at groups and their multiplication tables. Such quasigroups are constructed from a group using right division instead of multiplication. Their multiplication tables consist of circulant blocks which have additional symmetries and have a concise presentation. These tables are a r...

Given two n × n matrices A and B we want to compute their product c = A · B. The trivial algorithm runs in time n (this and the next running times are meant up to lower order factors n). In 1967 Strassen improved the running time to ≤ n and in 1990 Coppersmith and Winograd improved it further to ≤ n, which continues to be the best to date. Since the output is of size ≥ n it is clear that the be...

‎in [u‎. ‎dempwolff‎, ‎on extensions of elementary abelian groups of order $2^{5}$ by $gl(5,2)$‎, ‎textit{rend‎. ‎sem‎. ‎mat‎. ‎univ‎. ‎padova}‎, ‎textbf{48} (1972)‎, ‎359‎ - ‎364.] dempwolff proved the existence of a group of the‎ ‎form $2^{5}{^{cdot}}gl(5,2)$ (a non split extension of the‎ ‎elementary abelian group $2^{5}$ by the general linear group‎ ‎$gl(5,2)$)‎. ‎this group is the second l...

We show how to construct highly symmetric algorithms for matrix multiplication. In particular, we consider algorithms which decompose the matrix multiplication tensor into a sum of rank-1 tensors, where the decomposition itself consists of orbits under some finite group action. We show how to use the representation theory of the corresponding group to derive simple constraints on the decomposit...

Four-dimensional finite non-commutative associative algebras represent practical interest as algebraic support of post-quantum digital signature algorithms, especially with two sided global unit, set by sparse basis vectors multiplication tables. A new algebra the latter type, over field GF(p), is proposed and its structure investigated. The studied described a p2 + p 1 commutative subalgebras ...