Generalized column weights and equivalences of convolutional codes

We revisit the notion of rth generalized column weights for the j-truncation of a convolutional code. Taking the limit as j tends to infinity, we define rth generalized column weights of a convolutional code. We introduce suitable notions of j-equivalence and equivalence, with respect to which generalized column weights are code invariants. We establish some properties of these invariants and compare them with other definitions of generalized distance and weight which appear in the literature.