Published in Volume XXXIV, Issue 1, 2024, pages 23-38, doi: 10.47743/SACS.2024.1.23

Authors: S. Gannon, H. Kulosman

Abstract

We show that a necessary and sufficient condition for a cyclic code C of length N over a finite chain ring R (whose maximal ideal has nilpotence 2) to be an LCD code is that C = (f(x)), where f(X) is a self-reciprocal monic divisor of XN − 1 in R[X] and x = X + (XN − 1) in R[X]/(XN − 1). A similar, but slightly different, theorem was proved in 2019 by Z. Liu and J. Wang for general finite chain rings (Theorem 25 in [5]). We provide two proofs, both completely different than the proof of Liu and Wang.

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References

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Bibtex

@article{sacscuza:gannon2024ccclc,
  title={Classification of Certain Cyclic LCD Codes},
  author={S. Gannon, H. Kulosman},
  journal={Scientific Annals of Computer Science},
  volume={34},
  number={1},
  organization={Alexandru Ioan Cuza University, Ia\c si, Rom\^ania},
  year={2024},
  pages={23-38},
  publisher={Alexandru Ioan Cuza University Press, Ia\c si},
  doi={10.7561/SACS.2024.1.23}
}