Repeated-root cyclic and negacyclic codes over a finite chain ring

@article{Salagean2006RepeatedrootCA,
  title={Repeated-root cyclic and negacyclic codes over a finite chain ring},
  author={Ana Salagean},
  journal={Discrete Applied Mathematics},
  year={2006},
  volume={154},
  pages={413-419}
}
We show that repeated-root cyclic codes over a finite chain ring are in general not principally generated. Repeated-root negacyclic codes are principally generated if the ring is a Galois ring with characteristic a power of 2. For any other finite chain ring they are in general not principally generated. We also prove results on the structure, cardinality and Hamming distance of repeated-root cyclic and negacyclic codes over a finite chain ring. 

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Cyclic codes and minimal strong Gröbner bases over a principal ideal ring

  • G. H. Norton, A. Sălăgean
  • Finite Fields and Their Applications, 9:237–249,
  • 2003
Highly Influential
4 Excerpts

Canonical generating system of a monic polynomial ideal over a commutative artinian chain ring

  • A. A. Nechaev, D. A. Mikhailov
  • Discrete Math. Appl., 11:545–586,
  • 2001
3 Excerpts

Strong Gröbner bases for polynomials over a principal ideal ring

  • G. H. Norton, A. Sălăgean
  • Bull. of the Australian Mathematical Soc., 64:505…
  • 2001

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