Generators for repeated-root cyclic codes

Error-correcting codes were invented to correct errors on noisy communication channels. In the literature we often find the use of the Galois field Fnq of characteristic a prime p as the algebraic structure of choice. Even when this structure is algebraically handy, is hard to represent in a computer. Recently good quaternary codes, i.e. codes over Z4 , have been found and motivated the study of codes over rings in general. Traditionally, it is assumed that the codelength n is relatively prime to the characteristic p of the ring. In this thesis, we study a class of codes over Zpm for a prime p with codelength n = pdeltan¯ where p and n¯ are relatively prime. This codes are referred to as repeated-root cyclic codes. We have found generators for this codes and examples of good codes derived from them.