Relating propelinear and binary G-linear codes

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...

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Bibliographic Details
Published in:	Discrete mathematics Vol. 243; no. 1; pp. 187 - 194
Main Authors:	Alves, Marcelo M.S., Gerônimo, João R., Palazzo, Reginaldo, Costa, Sueli I.R., Interlando, J.Carmelo, Araújo, Martinho C.
Format:	Journal Article
Language:	English
Published:	Amsterdam Elsevier B.V 28-01-2002 Elsevier
Subjects:	[formula omitted]-linearity Applied sciences Binary codes Coding, codes Exact sciences and technology G-linearity Information, signal and communications theory Isometry groups Propelinear codes Signal and communications theory Telecommunications and information theory G-linearity Propelinear codes Isometry groups Z 4 -linearity Binary codes Hamming code Hamming metric Linear code Isometry Hamming distance Group theory G linearity Propelinear code Isometry group Binary code
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Summary:	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.
ISSN:	0012-365X 1872-681X
DOI:	10.1016/S0012-365X(01)00206-0