Upper bounds on weight hierarchies of extremal non-chain codes Original Research Article

The weight hierarchy of a linear [n,k;q] code C over GF(q) is the sequence (d1,d2,…,dk) where dr is the smallest support weight of an r-dimensional subcode of C. Linear codes may be classified according to a set of chain and non-chain conditions, the extreme cases being codes satisfying the chain condition (due to Wei and Yang) and extremal, non-chain codes (due to Chen and Kløve). This paper gives upper bounds on the weight hierarchies of the latter class of codes.