On the cosets of the simplex code
type: Item
instance of: scholarly article
title: On the cosets of the simplex code
zbMATH Open document ID: 0586.94017
DOI: 10.1016/0012-365X(85)90025-1
author: Tor Helleseth
author: H. F. jun. Mattson
published in: Discrete Mathematics
publication date: 1985-01-01T00:00:00Z
review text: Weight and distance properties of cosets of the simplex code are investigated. Let \(S_ m\) be the \((2^ m-1\), m, \(2^{m-1})\) simplex code and S its extension. It is shown that the coset of the all-1 vector of the extended code S of type \((2^ m\), m, \(2^{m-1})\) is the only coset of maximum weight \((2^{m-1})\). The same result is shown for the simplex code of type \((2^ m-1\), m, \(2^{m-1})\). Cosets of \(S_ m\) of weight one less than the maximum, \(2^{m-1}\), are studied. It is established that for \(m\geq 5\) there is no \((2d+1\), m, d) code with \(d\leq 2^{m-2}-2\) for which all vectors have weight at most \(2^{m-2}\). Cosets of weight \(2^{m-2}\) of \(S_ m\) are investigated and the cosets of \(S_ 5\) considered in some detail.
Mathematics Subject Classification ID: 94B05
zbMATH DE Number: 3941427
zbMATH Keywords: Weight and distance properties of cosets of the simplex code
reviewed by: Ian Blake
MaRDI profile type: Publication
cites work: A Bound for Error-Correcting Codes
cites work: Q4146667
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description: scientific article; zbMATH DE number 3941427