 The Euclidean algorithm also has other applications in error-correcting codes; for example, it can be used as an alternative to the Berlekamp–Massey algorithm for decoding BCH and Reed–Solomon codes, which are based on Galois fields.Euclid's algorithm can also be used to solve multiple linear Diophantine equations.Such equations arise in the Chinese remainder theorem, which describes a novel method to represent an integer "x".