Quaternary Delsarte-Goethals and Goethals-Delsarte codes
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.
scientific article; zbMATH DE number 1779461