Generalized Hamming Weights of Irreducible Cyclic Codes

The generalized Hamming weights d
_r
(C) of a linear code C are a natural generalization of the minimum Hamming distance d(C)[=d
₁
(C)] and have become an important research object in coding theory since Wei's originary work in 1991. In this paper, two general formulas on d(C) for irreducible cyclic codes are presented using Gauss sums and the weight hierarchy {d
₁
(C), d
₂
(C), ... , d
_k
(C)} (k= dim C) is completely determined for several cases.