New algorithms are presented for factoring polynomials of degree n over the finite field of q elements, where q is a power of a fixed prime number. When log q = n1+a , where a ...
We count the number of irreducible polynomials in several variables of a given degree over a finite field. The results are expressed in terms of a generating series, an exact for...
We study the polynomial reconstruction problem for low-degree multivariate polynomials over finite field F[2]. In this problem, we are given a set of points x ∈ {0, 1}n and ta...
Abstract. We present a Fourier-analytic approach to list-decoding Reed-Muller codes over arbitrary finite fields. We use this to show that quadratic forms over any field are locall...
Syntactical properties of representations of integers in various number systems are well-known and have been extensively studied. In this paper, we transpose the notion of recogniz...