Journal of Applied and Pure Mathematics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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ON THE CONSTRUCTION OF MDS SELF-DUAL CODES OVER GALOIS RINGS

  • Received : 2022.03.31
  • Accepted : 2022.05.23
  • Published : 2022.07.30
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Abstract

We study MDS(maximum distance separable) self-dual codes over Galois ring R = GR(2m, r). We prove that there exists an MDS self-dual code over R of length n if (n - 1) divides (2r - 1), and 2m divides n. We also provide the current state of the problem for the existence of MDS self-dual codes over Galois rings.

Keywords

Acknowledgement

The author thank the referees for their valuable comments which improved the clarity of this paper.

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