On Hamming Distance Distributions of Repeated-Root Cyclic Codes of Length 5p^s Over F_p ^m + uF_p ^m

Abstract

Let $p\not =5$ be any odd prime. Using the algebraic structures of all cyclic codes of length $5p^{s}$ over the finite commutative chain ring ${\mathcal{ R}}=\mathbb F_{p^{m}}+u\mathbb F_{p^{m}}$ , in this paper, the exact values of Hamming distances of all cyclic codes of length $5p^{s}$ over $\cal R$ are established. As an application, we identify all maximum distance separable cyclic codes of length $5p^{s}$ .

Keywords

• Constacyclic codes
• cyclic codes
• dual codes
• chain rings
• hamming distance
• singleton bound