# On cyclic codes over the ring $Z_p + uZ_p + ... + u^{k-1}Z_p$

@article{Singh2012OnCC, title={On cyclic codes over the ring \$Z\_p + uZ\_p + ... + u^\{k-1\}Z\_p\$}, author={Abhay Kumar Singh and Pramod Kumar Kewat}, journal={ArXiv}, year={2012}, volume={abs/1205.4148} }

In this paper, we study cyclic codes over the ring $ \Z_p + u\Z_p +...+ u^{k-1}\Z_p $, where $u^k =0$. We find a set of generator for these codes. We also study the rank, the dual and the Hamming distance of these codes.

## 3 Citations

### Complete classification of (δ + αu2)-constacyclic codes over F2m / < u4 > of oddly even length

- MathematicsDiscret. Math.
- 2017

### Cyclic codes over Z4[u]/ of odd length

- Computer ScienceArXiv
- 2016

The dual code of each cyclic code and self-dual cyclic codes over R of length n are investigated and a formula to count the number of codewords in each code is given.

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