A matrix ring description for cyclic convolutional codes

Heide Gluesing-Luerssen; Fai-Lung Tsang

doi:10.3934/amc.2008.2.55

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2008, Volume 2, Issue 1: 55-81. Doi: 10.3934/amc.2008.2.55

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A matrix ring description for cyclic convolutional codes

Heide Gluesing-Luerssen^1, and
Fai-Lung Tsang^2,

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

Received: July 31, 2007

Published: January 2008

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Abstract

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.

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Mathematics Subject Classification: Primary: 94B10, 94B15; Secondary: 16S36.

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