CYCLIC CODES OF LENGTH ps OVER Fpm[u] ⟨ue⟩
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초록
Let $R_e=\frac{\mathbb{F}_{p^m}[u]}{\langle u^e \rangle}$, where $p$ is a prime number, $ e $ is a positive integer and $u^e=0$. In this paper, we first characterize the structure of cyclic codes of length $p^s$ over $R_e$. These codes will be classified into $2^e $ distinct types. Among other results, in the case that $e=4$, the torsion codes of cyclic codes of length $ p^s $ over $ R_4$ are obtained. Also, we present some examples of cyclic codes of length $p^s $ over $R_e$.
Abstract
Let $R_e=\frac{\mathbb{F}_{p^m}[u]}{\langle u^e \rangle}$, where $p$ is a prime number, $ e $ is a positive integer and $u^e=0$. In this paper, we first characterize the structure of cyclic codes of length $p^s$ over $R_e$. These codes will be classified into $2^e $ distinct types. Among other results, in the case that $e=4$, the torsion codes of cyclic codes of length $ p^s $ over $ R_4$ are obtained. Also, we present some examples of cyclic codes of length $p^s $ over $R_e$.
참고문헌 (10)
- T. Abualrub, "Cyclic codes over the rings Z2 + uZ2 and Z2 + uZ2 + u2Z2", Des. Codes Cryptogr, 42(3), pp.273~287 (2007)[DOI]
- "⟨ue⟩ of Type 2", Finite Fields Appl, 55, pp.238~267 (2019)[DOI]
- H. Q. Dinh, "Negacyclic codes of length 2s over Galois rings", IEEE Trans. Inform. Theory, 51(12), pp.4252~4262 (2005)[DOI]
- H. Q. Dinh, "On the linear ordering of some classes of negacyclic and cyclic codes and their distance distributions", Finite Fields Appl, 14(1), pp.22~40 (2008)[DOI]
- H. Q. Dinh, "Constacyclic codes of length ps over Fpm + uFpm", J. Algebra, 324(5), pp.940~950 (2010)[DOI]
- ⟨ua⟩ and their duals, "Discrete Math", 2016, 1706~1715, 10.1016[DOI]
- H. Q. Dinh, "Cyclic and negacyclic codes over finite chain rings", IEEE Trans. Inform. Theory, 50(8), pp.1728~1744 (2004)[DOI]
- J. Gao, "Some results on cyclic codes over Zq + uZq", Discrete Math. Algorithms Appl, 7(4), pp.9~ (2015)[DOI]
- X. Liu, "A note on cyclic codes over Fpm + uFpm + u2Fpm", J. Math, 36(5) (2016)
- X. Liu, "Some classes of repeated-root constacyclic codes over Fpm +uFpm +u2Fpm", J. Korean Math. Soc, 51(4), pp.853~866 (2014)[DOI]