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

Julian Renner, Sven Puchinger, Antonia Wachter-Zeh, Camilla Hollanti, Ragnar Freij-Hollanti

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

1 Citation (Scopus)

Abstract

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 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.

Original languageEnglish
Title of host publication2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings
PublisherIEEE
Pages19-24
Number of pages6
ISBN (Electronic)9781728164328
DOIs
Publication statusPublished - Jun 2020
MoE publication typeA4 Article in a conference publication
EventIEEE International Symposium on Information Theory - Los Angeles, United States
Duration: 21 Jul 202026 Jul 2020

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
PublisherIEEE
Volume2020-June
ISSN (Print)2157-8095

Conference

ConferenceIEEE International Symposium on Information Theory
Abbreviated titleISIT
CountryUnited States
CityLos Angeles
Period21/07/202026/07/2020

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