Error control techniques for data sequences defined in finite integer rings

Abstract

We present results that can be used to design cyclic codes for data sequences defined in finite integer and complex integer rings. This follows from the previous work on generalization of the well-known Euler's theorem in finite integer rings and their polynomial extensions. The idea is to describe BCH and Reed-Solomon codes in these rings along with a decoding algorithm. The decoding algorithm in the ring employs the decoder in the finite field in an iterative manner. All the algebraic properties of the resulting codes follow from the underlying finite fields.