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On self-dual cyclic codes of length $p^a$ over $GR(p^2,s)$

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  • In this paper, cyclic codes over the Galois ring ${\rm GR}({p^2},s)$ are studied. The main result is the characterization and enumeration of Hermitian self-dual cyclic codes of length $p^a$ over ${\rm GR}({p^2},s)$. Combining with some known results and the standard Discrete Fourier Transform decomposition, we arrive at the characterization and enumeration of Euclidean self-dual cyclic codes of any length over ${\rm GR}({p^2},s)$.
    Mathematics Subject Classification: Primary: 94B15, 94B60; Secondary: 13B25.

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