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- W1574015443 abstract "In this paper, we have studied cyclic codes over the ring $R=mathbb{Z}_4+umathbb{Z}_4$, $u^2=0$. We have considered cyclic codes of odd lengths. A sufficient condition for a cyclic code over $R$ to be a $mathbb{Z}_4$-free module is presented. We have provided the general form of the generators of a cyclic code over $R$ and determined a formula for the ranks of such codes. In this paper we have mainly focused on principally generated cyclic codes of odd length over $R$. We have determined a necessary condition and a sufficient condition for cyclic codes of odd lengths over $R$ to be $R$-free." @default.
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- W1574015443 date "2015-01-06" @default.
- W1574015443 modified "2023-09-27" @default.
- W1574015443 title "Cyclic codes over $mathbb{Z}_4+umathbb{Z}_4$" @default.
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