On the construction of MRD convolutional codes

Abstract

The problem of building optimal block codes, such as MDS codes,over small fields has been an active area of research that led to sev-eral interesting conjectures. In the context of convolutional codes,optimal constructions, such as MDS or MDP, are very rare and allrequire very large finite fields. In this work, we focus on the problemof constructing optimal convolutional codes with respect to the rankdistance, i.e. we study the construction of Maximum Rank Distance(MRD) convolutional codes. Considering convolutional codes withina very general framework, we present concrete novel classes of MRDconvolutional codes for a large set of given parameters.