Encoding and Decoding Cyclic Code Groups

In this paper we show that the product of two cyclic codes with block lengths relatively prime can be described in terms of two interlaced codes. Using this description we provide an improved characterization of the generating polynomial of the product code in terms of the generating polynomials of the two original codes. We then show that the product code and seven other codes related to the product code (called a code group) can all be obtained from four canonical polynomials which may be calculated using the Euclidean Algorithm. These results then lead to simple encoder realizations for cyclic code groups and to a decoding algorithm, called cascade decoding.