A construction of MDS 2D convolutional codes of rate 1/n based on superregular matrices

Abstract

In this paper two-dimensional convolutional codes with finite support are considered, i.e., convolutional codes whose codewords have compact support indexed in N2 and take values in Fn, where F is a finite field. The main goal of this work is to analyze the (free) distance properties of this type of codes of rate 1/n and degree δ. We first establish an upper bound on the maximum possible distance for these codes. We then present particular constructions of two-dimensional convolutional codes with finite support of rate 1/n and degree δ that attain such a bound and therefore have the maximum distance among all two-dimensional convolutional codes with finite support with the same rate and degree. We call such codes maximum distance separable two-dimensional convolutional codes.