On the existence and construction of maximum distance profile convolutional codes

Abstract

[EN] In this paper, we study the conditions for a convolutional code to be MDP in terms of the size of the base field Fq as well as the openness of the MDP property in a given family of convolutional codes. Given (n, k, δ), our main result is an explicit bound depending on (n, k, δ)such that if q is greater than this bound, there exists a (n, k, δ)MDP convolutional code. A similar result is also offered for complete MDP convolutional codes. We show that these bounds are much lower than that those appeared so far in the literature. Finally, we show an explicit and simple construction procedure for MDP convolutional Goppa codes of dimension one.