The trace representation of the dual of quaternary Goethals code G (m) is given .It is proved that the shortened code of G (m) is cyclic and its generators are shown.
The 2-adic representations of codewords of the dual of quaternary Goethals code are given. By the 2-adic representations, the binary image of the dual of quaternary Goethals code under the Gray map is proved to be the...The 2-adic representations of codewords of the dual of quaternary Goethals code are given. By the 2-adic representations, the binary image of the dual of quaternary Goethals code under the Gray map is proved to be the nonlinear code constructed by Goethals in 1976.展开更多
The characteristic of Quaternary codes is analyzed. The rule of distinguishing triangle direction is given out. An algorithm of neighbor finding by decomposing the Quaternary code from back to front is presented in th...The characteristic of Quaternary codes is analyzed. The rule of distinguishing triangle direction is given out. An algorithm of neighbor finding by decomposing the Quaternary code from back to front is presented in this paper. The contrastive analysis of time complexity between this algorithm and Bartholdi＇s algorithm is approached. The result illustrates that the average consumed time of this algorithm is about 23.66% of Bartholdi＇s algorithm.展开更多
Let R=GR (4,m)be a Galois ring with Teichmuller set T_m and Tr_m be the trace function fromRto Z_4.In this paper,two classes of quaternary codes C_1 = {c(a,b):a ∈R,b ∈ T_(m/2)},where c(a,b)=(Tr_m(ax)+Tr_(m/2)(2 bx^(...Let R=GR (4,m)be a Galois ring with Teichmuller set T_m and Tr_m be the trace function fromRto Z_4.In this paper,two classes of quaternary codes C_1 = {c(a,b):a ∈R,b ∈ T_(m/2)},where c(a,b)=(Tr_m(ax)+Tr_(m/2)(2 bx^(2 m/2 +1)))_(x∈T_m),and C_2= {c(a,b):a ∈ R,b ∈ T_m}, where c(a,b)=(Tr_m(ax+2 bx^(2 k+1)))_(x∈T_m),and m/gcd(m,k)is even,are investigated,respectively.The Lee weight distributions,Hamming weight distributions and complete weight distributions of the codes are completely given.展开更多
Some properties such as type, trace description, symmetrized weight enumerator, and generalizedHamming weights of the dual of quaternary Goethals codes are discussed. Furthermore, the shortened codesof quaternary Goet...Some properties such as type, trace description, symmetrized weight enumerator, and generalizedHamming weights of the dual of quaternary Goethals codes are discussed. Furthermore, the shortened codesof quaternary Goethals codes and their dual codes are proved to be cyclic.展开更多
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The trace representation of the dual of quaternary Goethals code G (m) is given .It is proved that the shortened code of G (m) is cyclic and its generators are shown.
文摘The 2-adic representations of codewords of the dual of quaternary Goethals code are given. By the 2-adic representations, the binary image of the dual of quaternary Goethals code under the Gray map is proved to be the nonlinear code constructed by Goethals in 1976.
基金Supported by the Natural Science Foundation of China （No. 40771169 No.40471108 No.40701152）.
文摘The characteristic of Quaternary codes is analyzed. The rule of distinguishing triangle direction is given out. An algorithm of neighbor finding by decomposing the Quaternary code from back to front is presented in this paper. The contrastive analysis of time complexity between this algorithm and Bartholdi＇s algorithm is approached. The result illustrates that the average consumed time of this algorithm is about 23.66% of Bartholdi＇s algorithm.
文摘Let R=GR (4,m)be a Galois ring with Teichmuller set T_m and Tr_m be the trace function fromRto Z_4.In this paper,two classes of quaternary codes C_1 = {c(a,b):a ∈R,b ∈ T_(m/2)},where c(a,b)=(Tr_m(ax)+Tr_(m/2)(2 bx^(2 m/2 +1)))_(x∈T_m),and C_2= {c(a,b):a ∈ R,b ∈ T_m}, where c(a,b)=(Tr_m(ax+2 bx^(2 k+1)))_(x∈T_m),and m/gcd(m,k)is even,are investigated,respectively.The Lee weight distributions,Hamming weight distributions and complete weight distributions of the codes are completely given.
文摘Some properties such as type, trace description, symmetrized weight enumerator, and generalizedHamming weights of the dual of quaternary Goethals codes are discussed. Furthermore, the shortened codesof quaternary Goethals codes and their dual codes are proved to be cyclic.
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.
