The weight hierarchies of -ary linear codes of dimension 4

The weight hierarchy of a linear [ n , k ; q ] code C over G F ( q ) is the sequence ( d 1 , d 2 , … , d k ), where d r is the smallest support weight of an r -dimensional subcode of C . In this paper, by using the finite projective geometry method, we determine almost all weight hierarchies of q -ary general linear codes of dimension 4.