Searcharxiv⌕ Search

arXiv subjects

R. Smarandache

Publications and source records attributed to R. Smarandache.

2 recordsLinked to original sources
arXiv2006

Superregular Matrices and the Construction of Convolutional Codes having a Maximum Distance Profile

Superregular matrices are a class of lower triangular Toeplitz matrices that arise in the context of constructing convolutional codes having a maximum distance profile. These matrices are characterized by the property that no submatrix has a zero determinant unless it is trivially zero due to the lower triangular structure. In this paper, we discuss how superregular matrices may be used to construct codes having a maximum distance profile. We also introduce group actions that preserve the superregularity property and present an upper bound on the minimum size a finite field must have in order that a superregular matrix of a given size can exist over that field.

cs.IT↗
arXiv2003

Convolutional Codes with Maximum Distance Profile

Maximum distance profile codes are characterized by the property that two trajectories which start at the same state and proceed to a different state will have the maximum possible distance from each other relative to any other convolutional code of the same rate and degree. In this paper we use methods from systems theory to characterize maximum distance profile codes algebraically. Tha main result shows that maximum distance profile codes form a generic set inside the variety which parametrizes the set of convolutional codes of a fixed rate and a fixed degree.

math.OC↗