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

الأصل · EN

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 Fᵣ be an extension of a finite field Fq and r=qᵐ, we determine the weight distribution of the cyclic codes C={c(a, b): a, b ∈ Fᵣ}, c(a, b)=(Trᵣ/q(ag₁⁰+bg₂⁰),, Trᵣ/q(ag₁ⁿ⁻¹+bg₂ⁿ⁻¹)), g₁, g₂∈ Fᵣ, in the following two cases: (1) (g₁)=n, n|r-1 and g₂=1; (2) (g₁)=n, g₂=g₁², (g₂)= n 2, m=2 and 2(r-1)n|(q+1).