Section: New Results

Root-finding over Galois rings

Jérémy Berthomieu, Grégoire Lecerf and G. Quintin presented a new algorithm to find all the roots of a given polynomial with coefficients in a Galois ring [30] . It has been used to study the behavior of the Sudan algorithm for Reed-Solomon codes over Galois rings. The algorithm has been adapted to work over rings of power series in several variables. It was implemented in the Quintix package of Mathemagix.