In this paper, the quaternary Delsarte-Goethals code D(m,δ) and its dual code G(m,δ) are discussed. The type and the trace representation are given for D(m,δ), while the type and the minimum Lee weight are determin...In this paper, the quaternary Delsarte-Goethals code D(m,δ) and its dual code G(m,δ) are discussed. The type and the trace representation are given for D(m,δ), while the type and the minimum Lee weight are determined for G(m,δ). The shortened codes of D(m,δ) and G(m,δ) are proved to be 4-cyclic. The binary image of D(m,δ) is proved to be the binary Delsarte-Goethals code DG(m+1,δ),and the essential difference between the binary image of G(m,δ) and the binary Goethals-Delsarte codeGD(m+1,δ) is exhibited. Finally, the decoding algorithms of D■(m,δ) and G(m,δ) are discussed.展开更多
文摘In this paper, the quaternary Delsarte-Goethals code D(m,δ) and its dual code G(m,δ) are discussed. The type and the trace representation are given for D(m,δ), while the type and the minimum Lee weight are determined for G(m,δ). The shortened codes of D(m,δ) and G(m,δ) are proved to be 4-cyclic. The binary image of D(m,δ) is proved to be the binary Delsarte-Goethals code DG(m+1,δ),and the essential difference between the binary image of G(m,δ) and the binary Goethals-Delsarte codeGD(m+1,δ) is exhibited. Finally, the decoding algorithms of D■(m,δ) and G(m,δ) are discussed.
