On the Hamming Distance of Repeated-Root Cyclic Codes of Length 6 p s

Let <inline-formula> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> be an odd prime, <inline-formula> <tex-math notation="LaTeX">$s$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> be positive integers such that <inline-formula> <tex-math notation="LaTeX">$p^{m}\equiv 2 \pmod 3$ </tex-math></inline-formula>. In this paper, using the relationship about Hamming distances between simple-root cyclic codes and repeated-root cyclic codes, the Hamming distance of all cyclic codes of length <inline-formula> <tex-math notation="LaTeX">$6p^{s}$ </tex-math></inline-formula> over finite field <inline-formula> <tex-math notation="LaTeX">$\mathbb F_{p^{m}}$ </tex-math></inline-formula> is obtained. All maximum distance separable (MDS) cyclic codes of length <inline-formula> <tex-math notation="LaTeX">$6p^{s}$ </tex-math></inline-formula> are established.

Abstract licence: CC BY-NC-ND

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