Weight Hierarchies of Linear Codes Satisfying the Break-Chain Condition
Wende Chen · Beijing Youdian Xueyuan xuebao · 2004
The weight hierarchy of a linear [n,k;q] code C over GF(q) is the sequece (d_1, d_2, … d_k), where d_r is the 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 such codes are given. Further, by using the finite projective geometry method, explicit constructions of such codes are given, showing that in almost all cases, the necessary conditions are also sufficient by properly choosing the subspaces in the projective space. And so, almost all the weight hierarchies of such codes are determined.