Convolutional Codes With a Maximum Distance Profile Based on Skew Polynomials

We construct a family of
$(n,k)$
convolutional codes with degree
$\delta \in \{k,n-k\}$
that have a maximum distance profile. The field size required for our construction is
$\Theta (n^{2\delta })$
, which improves upon the known constructions of convolutional codes with a maximum distance profile. Our construction is based on the theory of skew polynomials.