Adaptive Binary Arithmetic coding is an effective mode of coding. In this paper we propose an efficient adaptive binary arithmetic coder, which is multiplication-free and look-up table free. To achieve this, we combine the probability estimation based on the virtual sliding window technique with the approximation of multiplication and the use of simple operations to calculate the next approxima...

This is the second in a series of papers on rank decompositions of the matrix multiplication tensor. We present new rank $23$ decompositions for the $3\times 3$ matrix multiplication tensor $M_{\langle 3\rangle}$. All our decompositions have symmetry groups that include the standard cyclic permutation of factors but otherwise exhibit a range of behavior. One of them has 11 cubes as summands and...

Multiple antennas can greatly increase the data rate and reliability of a wireless communica-tion link in a fading environment. It is well-known that unitary matrices can be used to designdi erentially modulated space-time constellations. These constellations have a particularly e -cient description if they form a nite group under matrix multiplication. In this paper we willshow...

We consider the bit-complexity of the problem stated in the title. Exact computations in algebraic number fields are performed symbolically. We present a polynomial-time algorithm to find a complete set of nonequivalent irreducible representations over the field of complex numbers of a finite group given by its multiplication table. In particular, it follows that some representative of each equ...

In this paper we present an algorithm for narrowing the constraint y = e x. The algorithm has been designed to be fast by using only IEEE multiplication. The main diiculty is to design algorithms which soundly, rapidly, and precisely compute upper and lower bounds on e x and ln(y). We prove that our algorithms are correct and produce upper and lower bounds which diier by at most 2 ULP. Experime...

An efficient method for generating a power of an operand, i.e., X p for an operand X and a given p, is proposed. It is applicable to ps in the form of ±2 k , where k is any integer and of ±2 1 k ± − 2 2 k , where k1 is any integer and k2 is any nonnegative integer. The reciprocal, the square root, the reciprocal square root, the reciprocal square, the reciprocal cube, and so forth are included....

the split extension group $a(4)cong 2^7{:}sp_6(2)$ is the affine subgroup of the symplectic group $sp_8(2)$ of index $255$‎. ‎in this paper‎, ‎we use the technique of the fischer-clifford matrices to construct the character table of the inertia group $2^7{:}(2^5{:}s_{6})$ of $a(4)$ of index $63$‎.

Non-Boolean computations implementing operations on multi-valued variables beyond base 2 allow enhanced computational complexity. We introduce DNA as a functional material for ternary computing, and in particular demonstrate the use of three-valued oligonucleotide inputs to construct a 3 × 3 multiplication table. The system consists of two three-valued inputs of -1; 0; +1 and a fluorophore/quen...

The divisors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. To pique the reader’s interest and curiosity let us pose the following riddle: what is an interesting number theoretic characterisation of the divisors of 24 amongst all positive integers? There are probably several characterisations of these numbers. In this paper I will provide one characterisation in terms of modular multiplication tables....

For integers, the parameter n is the bit-length, and for the finite field Fq we let n = log q. In the case of polynomial root-finding, d is the degree of the polynomial and we list bounds on the expected running time since these operations are most efficiently implemented using probabilistic algorithms. In Lecture 3 we addressed the cost of addition and subtraction in both Z and Fq, and the cos...