Algebraic coding techniques for data sequences defined over finite integer rings

This work establishes the design of BCH (Bose-Chaudhary-Hoquenghem) and RS (Reed Solomon) codes for processing data sequences defined over a ring of integers {0,1...,2^a-1}. The approach is to make use of the existing coding theory techniques over GF(2). The derivation of the generator polynomials over Z(2^a ) is based on expanding the corresponding generator polynomials defined over GF(2). The decoding procedure for the codes is also derived using the decoder over GF(2) recursively