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Structure and Rank of Cyclic codes over a class of non-chain rings
Nikita Jain, Sucheta Dutt, Ranjeet Sehmi · 2023-03-14 · via cs.IT updates on arXiv.org

The rings $Z_{4}+νZ_{4}$ have been classified into chain rings and non-chain rings on the basis of the values of $ν^{2} \in Z_{4}+νZ_{4}.$ In this paper, the structure of cyclic codes of arbitrary length over the rings $Z_{4}+νZ_{4}$ for those values of $ν^{2}$ 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.

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