Generalized column distances for convolutional codes

Abstract

In this work, we adapt the notion of generalized Hamming weight of block codes to introduce the novel concept of generalized column distances for convolutional codes. This can be considered as an extension of the work done in [18] on the generalized Hamming weights for free distance of convolutional codes. We also introduce the concept of Almost-MDP and NearMDP convolutional code. The problem of constructing convolutional codes with design generalized column distances remains an interesting open problem that requires further research.