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Structure and Rank of a Cyclic Code over a Class of Nonchain Rings

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  • Nikita Jain
  • Sucheta Dutt
  • Ranjeet Sehmi
  • Faranak Farshadifar

Abstract

The rings Z4+νZ4 have been classified into chain rings and nonchain rings based on the values of ν2∈Z4+νZ4. In this paper, the structure of a cyclic code of arbitrary length over the rings Z4+νZ4 for those values of ν2 for which these are nonchain rings has been established. A unique form of generators for a cyclic code over these rings has also been obtained. Furthermore, the rank and cardinality of a cyclic code over these rings have been established by finding a minimal spanning set for the code.

Suggested Citation

  • Nikita Jain & Sucheta Dutt & Ranjeet Sehmi & Faranak Farshadifar, 2024. "Structure and Rank of a Cyclic Code over a Class of Nonchain Rings," Journal of Mathematics, Hindawi, vol. 2024, pages 1-7, January.
    • Handle: RePEc:hin:jjmath:8817721
    DOI: 10.1155/2024/8817721
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