The Generalized Hamming Weight Hierarchy Of A Class Of Reducible Cyclic Codes

The generalized Hamming weight hierarchy of linear codes are fundamental para-menters,which have many applications in different aspects.The generalized Ham-ming weight hierarchy can completely characterize the performance of a linear code when it is used on wire-tap channel of type which is closely involved to its crypto-graphic property.In this thesis,we mainly utilize tools such as Gauss sums,character sums and Gauss periods to study the generalized Hamming weights for a class of re-ducible cyclic codes in the case of N even and e = t>2 and obtain partial results about the generalized Hamming weight hierarchy of the codes.We generalize the results of Xiong,Li and Ge in the case N = 1,2 and e = t ≥ 2.