Cyclic codes can easily be implemented in hardware and be decoded efficiently by means of algebraic methods. Though, for their actual minimum distance, which also determines their decoding radius, only lower bounds, such as the famous Bose-Ray-Chaudhuri-Hocquenghem (BCH) bound or the Hartmann-Tzeng bound, exist.
In this Master’s thesis, another approach for bounding the minimum distance of cyclic codes will be investigated, namely a concept that is based on embedding a cyclic code into another cyclic code in order to form a product code. A cyclic code of low rate and small minimum distance can be used for achieving a lower bound on the minimum distance of the other cyclic code.
Therefore, non-binary, non-primitive cyclic codes of minimum distances two and three will be analyzed. A condition that is both necessary and sufficient for a cyclic code to be of minimum distance two will be given. For cyclic codes of minimum distance three, some sufficient conditions are presented.
Due to the close connection to product codes, the defining set of cyclic product codes over prime fields will be determined.
The approach will be extended to using repeated-root cyclic codes for bounding the minimum distance of single-root cyclic codes, and vice versa. Hence, a condition that is both necessary and sufficient for a repeated-root cyclic code to be of minimum distance two is derived, and the defining set of the product code of a single-root cyclic code and a repeated-root cyclic code over a prime field is presented.