Structure and Rank of Cyclic codes over a class of non-chain rings

Nikita Jain; Sucheta Dutt; Ranjeet Sehmi

Structure and Rank of Cyclic codes over a class of non-chain rings

Information Theory 2023-03-15 v1 math.IT

Authors: Nikita Jain , Sucheta Dutt , Ranjeet Sehmi

Abstract

The rings $Z_{4}+\nu Z_{4}$ have been classified into chain rings and non-chain rings on the basis of the values of $\nu^{2} \in Z_{4}+\nu Z_{4}.$ In this paper, the structure of cyclic codes of arbitrary length over the rings $Z_{4}+\nu Z_{4}$ for those values of $\nu^{2}$ for which these are non-chain rings has been established. A unique form of generators of these codes has also been obtained. Further, rank and cardinality of these codes have been established by finding minimal spanning sets for these codes.

Keywords

cyclic codes non-chain rings code structure generators rank cardinality

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@article{arxiv.2303.07800,
  title  = {Structure and Rank of Cyclic codes over a class of non-chain rings},
  author = {Nikita Jain and Sucheta Dutt and Ranjeet Sehmi},
  journal= {arXiv preprint arXiv:2303.07800},
  year   = {2023}
}

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11 pages

Structure and Rank of Cyclic codes over a class of non-chain rings

Abstract

Keywords

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