Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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CYCLIC CODES OF LENGTH ps OVER $\frac{{\mathbb{F}}_{p^m}[u]}{{\langle}u^e{\rangle}}$

  • Received : 2023.03.15
  • Accepted : 2023.07.03
  • Published : 2024.01.31
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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 ue = 0. In this paper, we first characterize the structure of cyclic codes of length ps over Re. These codes will be classified into 2e distinct types. Among other results, in the case that e = 4, the torsion codes of cyclic codes of length ps over R4 are obtained. Also, we present some examples of cyclic codes of length ps over Re.

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References

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