Generalized Hamming Weights of Irreducible Cyclic Codes
Abstract
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.
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