# American Institute of Mathematical Sciences

February  2008, 2(1): 55-81. doi: 10.3934/amc.2008.2.55

## A matrix ring description for cyclic convolutional codes

 1 Department of Mathematics, University of Kentucky, 715 Patterson Office Tower, Lexington, KY 40506-0027, United States 2 Department of Mathematics, University of Groningen, P. O. Box 407, 9700 AK Groningen, Netherlands

Received  August 2007 Published  January 2008

In this paper, we study convolutional codes with a specific cyclic structure. By definition, these codes are left ideals in a certain skew polynomial ring. Using that the skew polynomial ring is isomorphic to a matrix ring we can describe the algebraic parameters of the codes in a more accessible way. We show that the existence of such codes with given algebraic parameters can be reduced to the solvability of a modified rook problem. It is our strong belief that the rook problem is always solvable, and we present solutions in particular cases.
Citation: Heide Gluesing-Luerssen, Fai-Lung Tsang. A matrix ring description for cyclic convolutional codes. Advances in Mathematics of Communications, 2008, 2 (1) : 55-81. doi: 10.3934/amc.2008.2.55
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