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Title: A matrix based list decoding algorithm for linear codes over integer residue rings
Author: Napp, Diego
Pinto, Raquel
Saçıkara, Elif
Toste, Marisa
Keywords: Finite rings
Linear codes over finite rings
Erasure channel
Decoding algorithms
Matrix representations
Parity-check matrix
Issue Date: 1-Apr-2021
Publisher: Elsevier
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.
Peer review: yes
DOI: 10.1016/j.laa.2020.09.031
ISSN: 0024-3795
Appears in Collections:CIDMA - Artigos
DMat - Artigos
SCG - Artigos

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