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Relating propelinear and binary G-linear codes

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Repositório Institucional UNESP
Keywords
  • Binary Codes
  • Z(4)-Linearity
  • Propelinear Codes
  • Isometry Groups
  • G-Linearity
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Abstract

In this paper we establish the connections between two different extensions of Z(4)-linearity for binary Hamming spaces, We present both notions - propelinearity and G-linearity - in the context of isometries and group actions, taking the viewpoint of geometrically uniform codes extended to discrete spaces. We show a double inclusion relation: binary G-linear codes are propelinear codes, and translation-invariant propelinear codes are G-linear codes. (C) 2002 Elsevier B.V. B.V. All rights reserved.

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