Let P(n) denote the largest prime divisor of n, and let (x, y) be the number of integers n x with P(n) y. In this paper we present improvements to Bernstein's algorithm, whi...
We present a parallel algorithm for exact division of sparse distributed polynomials on a multicore processor. This is a problem with significant data dependencies, so our solutio...
In 1974, Johnson showed how to multiply and divide sparse polynomials using a binary heap. This paper introduces a new algorithm that uses a heap to divide with the same complexit...
This paper presents a list-decoding algorithm for classical irreducible binary Goppa codes. The algorithm corrects, in polynomial time, approximately n − p n(n − 2t − 2) err...
Computing only the low degree terms of the product of two univariate polynomials is called a short multiplication. By decomposition into subproblems, a short multiplication can be ...