A construction of the generators of cyclic codes over Zm and related results.

摘要

The need for good codes has motivated most of the research in the theory of error-correcting codes. Codes have been constructed mostly over the finite field $Z2$. In the last decade or so, good codes over the finite rings $Zm$ have been found. In this thesis, in addition to some results on cyclic codes and their primitive idempotents, we find a construction of the generators of cyclic codes over $Zm$, and thus find a way of obtaining all cyclic codes of length n over finite rings of integers $Zm$.