Abstract—This paper generalizes the classical Knuth–Schönhage algorithm computing the greatest common divisor (gcd) of two polynomials for solving arbitrary linear Diophantine...
In this paper we propose an improved algorithm for finding roots of polynomials over finite fields. This makes possible significant speed up of the decoding process of BCH, Reed-S...
: We develop a framework for solving polynomial equations with size constraints on solutions. We obtain our results by showing how to apply a technique of Coppersmith for finding ...
We give a polynomial time construction of binary codes with the best currently known trade-off between rate and error-correction radius. Specifically, we obtain linear codes ove...