On the Hamming distances of repeated-root cyclic codes of length 5p^s
share
Due to the wide applications in consumer electronics, data storage systems and communication systems, cyclic codes have been an interesting research topic in coding theory. In this paper, let p be a prime with p> 7. We determine the weight distributions of all cyclic codes of length 5 over _q and the Hamming distances of all repeated-root cyclic codes of length 5p^s over _q, where q=p^m and both s and m are positive integers. Furthermore, we find all MDS cyclic codes of length 5p^s and take quantum synchronizable codes from repeated-root cyclic codes of length 5p^s.
READ FULL TEXT