A matrix based list decoding algorithm for linear codes over integer residue rings

• Autor(a) principal: Napp, Diego
• Data de Publicação: 2021
• Outros Autores: Pinto, Raquel, Saçıkara, Elif, Toste, Marisa
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10773/30499
• topic: Finite rings; Linear codes over finite rings; Erasure channel; Decoding algorithms; Matrix representations; Parity-check matrix

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.