Abstract: The weight hierarchy of a linear [n,k;q] codeC over GF(q) is the sequece (d₁, d₂, … d_k), where d_r isthe smallest support weight of an r-dimensional subcode of C. The weight hierarchies of linear codes satisfying the break-chain condition containing many abutal break points of general dimension over GF(q) are investigated. First,a simple necessary condition for a sequence to be the weight hierarchies of suchcodes are given. Further, by using the finite projective geometry method, explicit constructions of such codes are given, showing that in almost all cases, thenecessary conditions are also sufficient by properly choosing the subspaces inthe projective space. And so, almost all the weight hierarchies of such codes are determined.

Key words: weight hierarchy, deference sequence, break-chain condition.