Quaternary Delsarte-Goethals and Goethals-Delsarte codes
type: Item
instance of: scholarly article
title: Quaternary Delsarte-Goethals and Goethals-Delsarte codes
zbMATH Open document ID: 1004.94037
author: Jie Cui
author: Zhe-Xian Wan
published in: Journal of Systems Science and Complexity
publication date: 2003-02-02T00:00:00Z
review text: This paper is a continuation of the work by \textit{Ciu Jie} and \textit{Pei Junying} [Appl. Math., Ser. B 16, 81-87 (2001; Zbl 1004.94035)]. The quaternary Goethals-Delsarte code and its dual are studied. Type and trace representation are determined. For the dual code, the minimum Lee weight is determined. The shortened codes are proved to be cyclic. The binary Delsarte-Goethals codes are proved to be the binary images of the quaternary Delsarte-Goethals codes, while it is shown that the binary Goethals-Delsarte codes (duals of Delsarte-Goethals codes) are not the binary images of the quaternary Goethals-Delsarte codes (i.e. the duals of the quaternary Delsarte-Goethals codes). Furthermore some attention is paid to decoding algorithms for the above-mentioned quaternary codes.
Mathematics Subject Classification ID: 94B60
Mathematics Subject Classification ID: 94B15
Mathematics Subject Classification ID: 94B35
zbMATH DE Number: 1779461
zbMATH Keywords: quaternary Goethals-Delsarte code
zbMATH Keywords: trace representation
zbMATH Keywords: minimum Lee weight
zbMATH Keywords: quaternary Delsarte-Goethals codes
zbMATH Keywords: decoding algorithms
reviewed by: Herman J. Tiersma
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1779461