Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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FREE CYCLIC CODES OVER FINITE LOCAL RINGS

  • Woo, Sung-Sik (DEPARTMENT OF MATHEMATICS, EWHA WOMEN'S UNIVERSITY)
  • Published : 2006.11.30
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Abstract

In [2] it was shown that a 1-generator quasi-cyclic code C of length n = ml of index l over $\mathbb{Z}_4$ is free if C is generated by a polynomial which divides $X^m-1$. In this paper, we prove that a necessary and sufficient condition for a cyclic code over $\mathbb{Z}_pk$ of length m to be free is that it is generated by a polynomial which divides $X^m-1$. We also show that this can be extended to finite local rings with a principal maximal ideal.

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References

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Cited by

  1. On quasi-cyclic codes over $${\mathbb{Z}_q}$$ vol.20, pp.5-6, 2009, https://doi.org/10.1007/s00200-009-0110-8
  2. IDEALS OF Zpn[X]/(Xl-1) vol.26, pp.3, 2011, https://doi.org/10.4134/CKMS.2011.26.3.427
  3. CYCLIC CODES OF LENGTH 2nOVER ℤ4 vol.28, pp.1, 2013, https://doi.org/10.4134/CKMS.2013.28.1.039