Climent, Joan-Josep, Napp, Diego, Perea, Carmen, Pinto, Raquel
A construction of MDS 2D convolutional codes of rate 1/n based on superregular matrices
Linear Algebra and its Applications. 2012, 437(3): 766-780. doi:10.1016/j.laa.2012.02.032
URI: http://hdl.handle.net/10045/34679
DOI: 10.1016/j.laa.2012.02.032
ISSN: 0024-3795 (Print)
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.
Keywords:2D convolutional code, Code distance, MDS convolutional code, Superregular matrix, Cauchy matrix
Elsevier
info:eu-repo/semantics/article