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We prove several results on the generalized Hamming weights (GHW's) of linear codes, particularly for cyclic codes. Based on these and previously known results, we give some efficient algorithms for computing GHW hierarchy of cyclic codes. We give complete weight hierarchy for each of the binary cyclic codes of odd lengths Š31. A table of second and third GHW's of binary cyclic codes of odd lengths Š57 is also presented. We have also computed the second GHW of all binary cyclic codes of length 63 and the third GHW of one code from each dimension. Index terms - Generalized Hamming weights, cyclic codes, Mathematica, chain condition, generalized Griesmer bound, algorithm
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