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Type: Artigo
Title: A construction of F2-linear cyclic, MDS codes
Author: Cardell, Sara D.
Climent, Joan-Josep
Panario, Daniel
Stevens, Brett
Abstract: In this paper we construct F2-linear codes over Fb2 with length n and dimension n−r where n=rb. These codes have good properties, namely cyclicity, low density parity-check matrices and maximum distance separation in some cases. For the construction, we consider an odd prime p, let n=p−1 and utilize a partition of Zn. Then we apply a Zech logarithm to the elements of these sets and use the results to construct an index array which represents the parity-check matrix of the code. These codes are always cyclic and the density of the parity-check and the generator matrices decreases to 0 as n grows (for a fixed r). When r=2 we prove that these codes are always maximum distance separable. For higher r some of them retain this property
Subject: Matrizes (Matemática)
Country: Estados Unidos
Editor: American Institute of Mathematical Sciences
Rights: Fechado
Identifier DOI: 10.3934/amc.2020047
Date Issue: 2020
Appears in Collections:IMECC - Artigos e Outros Documentos

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