Weight distributions of cyclic codes with respect to pairwise coprime order elements

Chengju Li, Qin Yue, Fengwei Li

Let ${\mathbb{F}}_r$ be an extension of a finite field ${\mathbb{F}}_q$ with $r=q^m$. Let each $g_i$ be of order $n_i$ in ${\mathbb{F}}_r^{\ast }$ and $\gcd (n_i,n_j)=1$ for $1\le i\ne j\le u$. We de…