Generalized column weights and equivalences of convolutional codes

Abstract

We revisit the notion of [Formula: see text]th generalized column weights for the [Formula: see text]-truncation of a convolutional code. Taking the limit as [Formula: see text] tends to infinity, we define [Formula: see text]th generalized column weights of a convolutional code. We introduce suitable notions of [Formula: see text]-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.