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

Xia Li; Qin Yue

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arXiv · 1911.07542

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

Xia Li·Qin Yue

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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 $p\ge 7$. 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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Xia Li, Qin Yue. 2019-11-18. On the Hamming distances of repeated-root cyclic codes of length $5p^s$. https://arxiv.org/abs/1911.07542

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