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Paper IDA.1.4
Paper Title Low-Rank Parity-Check Codes over the Ring of Integers Modulo a Prime Power
Authors Julian Renner, Technical University of Munich, Germany; Sven Puchinger, Technical University of Denmark, Denmark; Antonia Wachter-Zeh, Technical University of Munich, Germany; Camilla Hollanti, Ragnar Freij-Hollanti, Aalto University, Finland
Session A.1: Algebraic Coding Theory I
Presentation Lecture
Track Algebraic and Combinatorial Coding Theory
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Abstract We define and analyze low-rank parity-check (LRPC) codes over extension rings of the finite chain ring $\ZZ_{p^r}$, 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 coding. We give a decoding algorithm based on simple linear-algebraic operations. Further, we derive an upper bound on the failure probability of the decoder. The upper bound is valid for errors whose rank is equal to the free rank.

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2021 IEEE International Symposium on Information Theory

11-16 July 2021 | Melbourne, Victoria, Australia

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