Low-Rank Parity-Check Codes over the Ring of Integers Modulo a Prime Power

@article{Renner2020LowRankPC,
  title={Low-Rank Parity-Check Codes over the Ring of Integers Modulo a Prime Power},
  author={Julian Renner and Sven Puchinger and Antonia Wachter-Zeh and Camilla Hollanti and Ragnar Freij},
  journal={2020 IEEE International Symposium on Information Theory (ISIT)},
  year={2020},
  pages={19-24}
}
We define and analyze low-rank parity-check (LRPC) codes over extension rings of the finite chain ring ${{\mathbb{Z}}_{{p^r}}}$, where p is a prime and r is a positive integer. LRPC codes have originally been proposed by Gaborit et al. (2013) over finite fields for cryptographic applications. The adaption to finite rings is inspired by a recent paper by Kamche et al. (2019), which constructed Gabidulin codes over finite principle ideal rings with applications to space-time codes and network… Expand
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