Two Classes of Quaternary Codes from Z<sub>4</sub>-valued Quadratic Forms

doi:10.16356/j.1005-1120.2018.05.896

Transactions of Nanjing University of Aeronautics & Astronautics

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Archive > Volume 35 Issue 5 > 2018,35(5):896-912. DOI:10.16356/j.1005-1120.2018.05.896 Prev Next

Two Classes of Quaternary Codes from Z₄-valued Quadratic Forms

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Abstract:

Let R=GR(4,m) be a Galois ring with Teichmuller set T_m and Tr_m be the trace function from R to Z₄. In this paper, two classes of quaternary codes C₁={c(a,b):a∈R,b∈T_m/2}, where c(a,b)=(Tr_m(ax)+Tr_m/2(2bx^{2^m/2}+1))_{x∈T_m}, and C₂={c(a,b):a∈R,b∈T_m}, where c(a,b)=(Tr_m(ax+2bx^{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.

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