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

03/14/2023

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by   Nikita Jain, et al.

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The rings Z_4+ν Z_4 have been classified into chain rings and non-chain rings on the basis of the values of ν^2∈ Z_4+ν Z_4. In this paper, the structure of cyclic codes of arbitrary length over the rings Z_4+ν Z_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.