Weight distribution of two classes of cyclic codes with respect to two distinct order elements

Abstract

Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. Cyclic codes have been studied for many years, but their weight distribution are known only for a few cases. In this paper, let ${\mathbb{F}}_r$ be an extension of a finite field ${\mathbb{F}}_q$ and $r=q^m$, we determine the weight distribution of the cyclic codes $\mathcal{C}=\{c(a,b):a,b\in {\mathbb{F}}_r\},$ $$c(a, b)=(\mbox {Tr}_{r/q}(ag_1^0+bg_2^0), \ldots, \mbox {Tr}_{r/q}(ag_1^{n-1}+bg_2^{n-1})), g_1, g_2\in \Bbb F_r,$$ in the following two cases: (1) $\ord(g_1)=n, n|r-1$ and $g_2=1$; (2) $\ord(g_1)=n$, $g_2=g_1^2$, $\ord(g_2)=\frac n 2$, $m=2$ and $\frac{2(r-1)}{n}|(q+1)$.

References in corpus (1)

• The Weight Distribution of a Class of Cyclic Codes Related to Hermitian Forms Graphs

Cited by in corpus (1)

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