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Generalized Hamming Weights of Irreducible Cyclic Codes (1410.2702v1)
Published 10 Oct 2014 in cs.IT and math.IT
Abstract: The generalized Hamming weight (GHW) $d_r(C)$ of linear codes $C$ is a natural generalization of the minimum Hamming distance $d(C)(=d_1(C))$ 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 $d_r(C)$ for irreducible cyclic codes are presented by using Gauss sums and the weight hierarchy ${d_1(C), d_2(C), \ldots, d_k(C)}$ $(k=\dim C)$ are completely determined for several cases.