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 /spl les/31. A table of second and third GHW's of binary cyclic codes of odd lengths /spl les/57 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.

A (55,16,19) binary Goppa code is used to construct (57,17,17), (58,17,18), (59,17,19), and (60,17,20) codes. The first two codes have smaller redundancy than previously known codes (linear or nonlinear) of the same length and minimum distance. The last two codes have parameters previously attained only by nonlinear codes.>

A Griesmer-like upper bound on the covering radius, R, is given. To the author's knowledge this is the only upper bound which explicitly depends on all three parameters n, k, and d. An upper bound on R for cyclic codes is then given which depends on the generator polynomial of the cyclic code and which, in many cases, leads to an improvement of the previous bound. An upper bound on the irreducible generator polynomial cyclic codes is also given. New interpretations and applications of the so-called Norse bounds and necessary and sufficient conditions to attain one of these bounds are provided. Generalizations of most of the results for codes over GF(q) are outlined.>