On the Hamming distances of repeated-root cyclic codes of length 5p^s

2019/11/18 by Xia Li, Qin Yue, Li, Xia +1
Computer Science · Engineering · Mathematics · #Cellular Automata and Applications #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #graph theory and CDMA systems #math.IT

paper · pdf · doi:10.48550/arxiv.1911.07542

21 pages

openalex publication_date 2019/11/18 · arxiv created 2019/11/20 · arxiv updated 2019/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 weight distributions of all cyclic codes of length 5 over \f_q and the Hamming distances of all repeated-root cyclic codes of length 5p^s over \F_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.

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