Generalized Hamming Weights of Irreducible Cyclic Codes

الأصل · EN

The generalized Hamming weight (GHW) dᵣ(C) of linear codes C is a natural generalization of the minimum Hamming distance d(C)(=d₁(C)) and has become one of important research objects in coding theory since Wei's originary work [23] in 1991. In this paper two general formulas on dᵣ(C) for irreducible cyclic codes are presented by using Gauss sums and the weight hierarchy {d₁(C), d₂(C),, dₖ(C)} (k= C) are completely determined for several cases.