The Weight Distributions of a Class of Cyclic Codes with Three Nonzeros over 𝔽₃

Table 1

Irreducible components corresponding to the projective variety defined by (19).

𝑥^2,	𝑥^2,	𝑥^2,	𝑥^2,	𝑥^2,	𝑥^2,	𝑥^2,	𝑥^2,
𝑦−𝑤−𝑢,	𝑦−𝑤−𝑢,	𝑦−𝑤+𝑢,	𝑦−𝑤+𝑢,	𝑦+𝑤−𝑢,	𝑦+𝑤−𝑢,	𝑦+𝑤+𝑢,	𝑦+𝑤+𝑢,
𝑧−𝑤+𝑢,	𝑧+𝑤−𝑢,	𝑧−𝑤−𝑢,	𝑧+𝑤+𝑢,	𝑧−𝑤−𝑢,	𝑧+𝑤+𝑢,	𝑧−𝑤+𝑢,	𝑧+𝑤−𝑢,
𝑦^2,	𝑦^2,	𝑦^2,	𝑦^2,	𝑦^2,	𝑦^2,	𝑦^2,	𝑦^2,
𝑥−𝑤−𝑢,	𝑥−𝑤−𝑢,	𝑥−𝑤+𝑢,	𝑥−𝑤+𝑢,	𝑥+𝑤−𝑢,	𝑥+𝑤−𝑢,	𝑥+𝑤+𝑢,	𝑥+𝑤+𝑢,
𝑧−𝑤+𝑢,	𝑧+𝑤−𝑢,	𝑧−𝑤−𝑢,	𝑧+𝑤+𝑢,	𝑧−𝑤−𝑢,	𝑧+𝑤+𝑢,	𝑧−𝑤+𝑢,	𝑧+𝑤−𝑢,
𝑧^2,	𝑧^2,	𝑧^2,	𝑧^2,	𝑧^2,	𝑧^2,	𝑧^2,	𝑧^2,
𝑥−𝑤−𝑢,	𝑥−𝑤−𝑢,	𝑥−𝑤+𝑢,	𝑥−𝑤+𝑢,	𝑥+𝑤−𝑢,	𝑥+𝑤−𝑢,	𝑥+𝑤+𝑢,	𝑥+𝑤+𝑢,
𝑦−𝑤+𝑢,	𝑦+𝑤−𝑢,	𝑦−𝑤−𝑢,	𝑦+𝑤+𝑢,	𝑦−𝑤−𝑢,	𝑦+𝑤+𝑢,	𝑦−𝑤+𝑢,	𝑦+𝑤−𝑢,
𝑤^2,	𝑤^2,	𝑤^2,	𝑤^2,	𝑤^2,	𝑤^2,	𝑤^2,	𝑤^2,
𝑥−𝑧−𝑢,	𝑥−𝑧−𝑢,	𝑥−𝑧+𝑢,	𝑥−𝑧+𝑢,	𝑥+𝑧−𝑢,	𝑥+𝑧−𝑢,	𝑥+𝑧+𝑢,	𝑥+𝑧+𝑢,
𝑦−𝑧+𝑢,	𝑦+𝑧−𝑢,	𝑦−𝑧−𝑢,	𝑦+𝑧+𝑢,	𝑦−𝑧−𝑢,	𝑦+𝑧+𝑢,	𝑦−𝑧+𝑢,	𝑦+𝑧−𝑢,
𝑢^2,	𝑢^2,	𝑢^2,	𝑢^2,	𝑢^2,	𝑢^2,	𝑢^2,	𝑢^2,
𝑥−𝑧−𝑤,	𝑥−𝑧−𝑤,	𝑥−𝑧+𝑤,	𝑥−𝑧+𝑤,	𝑥+𝑧−𝑤,	𝑥+𝑧−𝑤,	𝑥+𝑧+𝑤,	𝑥+𝑧+𝑤,
𝑦−𝑧+𝑤,	𝑦+𝑧−𝑤,	𝑦−𝑧−𝑤,	𝑦+𝑧+𝑤,	𝑦−𝑧−𝑤,	𝑦+𝑧+𝑤,	𝑦−𝑧+𝑤,	𝑦+𝑧−𝑤,