Abstract
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 Hamming distances of all repeated-root cyclic codes of length 5ps over Fq, where q=pm and both s and m are positive integers. Furthermore, we find all MDS cyclic codes of length 5ps and take quantum synchronizable codes from repeated-root cyclic codes of length 5ps. By comparing the minimum distances of 5ps-length repeated-root cyclic codes to BCH codes of close lengths, we illustrated that quantum synchronizable codes constructed from repeated-root cyclic codes have in general better performance in correcting Pauli errors than those from BCH codes.
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