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http://hdl.handle.net/10773/30499
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DC Field | Value | Language |
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dc.contributor.author | Napp, Diego | pt_PT |
dc.contributor.author | Pinto, Raquel | pt_PT |
dc.contributor.author | Saçıkara, Elif | pt_PT |
dc.contributor.author | Toste, Marisa | pt_PT |
dc.date.accessioned | 2021-02-05T13:02:44Z | - |
dc.date.available | 2021-02-05T13:02:44Z | - |
dc.date.issued | 2021-04-01 | - |
dc.identifier.issn | 0024-3795 | pt_PT |
dc.identifier.uri | http://hdl.handle.net/10773/30499 | - |
dc.description.abstract | In this paper we address the problem of list decoding of linear codes over an integer residue ring Zq, where q is a power of a prime p. The proposed procedure exploits a particular matrix representation of the linear code over Zpr , called the standard form, and the p-adic expansion of the to-be-decoded vector. In particular, we focus on the erasure channel in which the location of the errors is known. This problem then boils down to solving a system of linear equations with coefficients in Zpr . From the parity-check matrix representations of the code we recursively select certain equations that a codeword must satisfy and have coefficients only in the field p^{r−1}Zpr . This yields a step by step procedure obtaining a list of the closest codewords to a given received vector with some of its coordinates erased. We show that such an algorithm actually computes all possible erased coordinates, that is, the provided list is minimal. | pt_PT |
dc.language.iso | eng | pt_PT |
dc.publisher | Elsevier | pt_PT |
dc.relation | UIDB/04106/2020 | pt_PT |
dc.relation | UIDP/04106/2020 | pt_PT |
dc.rights | embargoedAccess | pt_PT |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | pt_PT |
dc.subject | Finite rings | pt_PT |
dc.subject | Linear codes over finite rings | pt_PT |
dc.subject | Erasure channel | pt_PT |
dc.subject | Decoding algorithms | pt_PT |
dc.subject | Matrix representations | pt_PT |
dc.subject | Parity-check matrix | pt_PT |
dc.title | A matrix based list decoding algorithm for linear codes over integer residue rings | pt_PT |
dc.type | article | pt_PT |
dc.description.version | published | pt_PT |
dc.peerreviewed | yes | pt_PT |
degois.publication.firstPage | 376 | pt_PT |
degois.publication.lastPage | 393 | pt_PT |
degois.publication.title | Linear Algebra and its Applications | pt_PT |
degois.publication.volume | 614 | pt_PT |
dc.date.embargo | 2023-04-01 | - |
dc.identifier.doi | 10.1016/j.laa.2020.09.031 | pt_PT |
Appears in Collections: | CIDMA - Artigos DMat - Artigos SCG - Artigos |
Files in This Item:
File | Description | Size | Format | |
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List_Decoding_Revised_Version_FINAL.pdf | 284.24 kB | Adobe PDF | View/Open |
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