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CYCLIC CODES OF LENGTH 2n OVER ℤ4

Woo, Sung Sik

  • Received : 2012.01.12
  • Published : 2013.01.31

Abstract

The purpose of this paper is to find a description of the cyclic codes of length $2^n$ over $\mathbb{Z}_4$. We show that any ideal of $\mathbb{Z}_4$[X]/($X^{2n}$ - 1) is generated by at most two polynomials of the standard forms. We also find an explicit description of their duals in terms of the generators.

Keywords

cyclic code over $\mathbb{Z}_4$

References

  1. P. Kanwar and S. R. Lopez-Permouth, Cyclic codes over the integers modulo pm, Finite Fields Appl. 3 (1997), no. 4, 334-352. https://doi.org/10.1006/ffta.1997.0189
  2. Bernard R. McDonald, Finite Rings with Identity, Marcel Dekker, 1974.
  3. S. S. Woo, Free cyclic codes over finite local rings, Bull. Korean Math. Soc. 43 (2006), no. 4, 723-735. https://doi.org/10.4134/BKMS.2006.43.4.723
  4. S. S. Woo, Ideals of ${\mathbb{Z}}_p^n[X]/(X^l-1)$, Commun. Korean Math. Soc. 26 (2011), no. 3, 427-443. https://doi.org/10.4134/CKMS.2011.26.3.427
  5. S. S. Woo, Cyclic codes of even length over ${\mathbb{Z}}_4$, J. Korean Math. Soc. 44 (2007), no. 3, 697-706. https://doi.org/10.4134/JKMS.2007.44.3.697
  6. M. F. Atiyah and I. G. Macdonald, Introduction to Commutative algebra, Addison-Wesley, 1969.
  7. S. T. Dougherty and Y. H. Park, On modular cyclic codes, Finite Fields Appl. 13 (2007), no. 1, 31-57. https://doi.org/10.1016/j.ffa.2005.06.004