Some results on the Hamming distances of cyclic codes

Cyclic codes over finite fields have been studied for decades due to their wide applicability in communication systems, consumer electronics, and data storage systems. Let p be an odd prime and let s and m be positive integers. In this paper, we first determine the Hamming distances of all cyclic codes of length 8 over \(F_q\) $F_q$ . Building upon this, we explicitly obtain the Hamming distances of all repeated-root cyclic codes of length \(8p^s\) $8p^s$ over \(F_q\) $F_q$ . As an application, we give all maximum distance separable cyclic codes of length \(8p^s\) $8p^s$ .