Self-dual codes over a family of local rings

Steven T. Dougherty*, Cristina Fernández-Córdoba, Roger Ten-Valls

*Corresponding author for this work

Research output: Contribution to journalArticleResearchpeer-review

Abstract

We construct an infinite family of commutative rings Rq,Δ and we study codes over these rings as well as the structure of the rings. We define a canonical Gray map from Rq,Δ to vectors over the residue finite field of q elements and use it to relate codes over Rq,Δ to codes over the finite field Fq. Finally, we determine the parameters for when self-dual codes exist and give various constructions for self-dual codes over Rq,Δ.

Original languageEnglish
JournalApplicable Algebra in Engineering, Communications and Computing
DOIs
Publication statusAccepted in press - 2020

Keywords

  • Codes over rings
  • Local rings
  • Self-dual codes

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