摘要
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.
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.
