A Matrix Ring Description for Cyclic Convolutional Codes

Details A Matrix Ring Description for Cyclic Convolutional Codes A Matrix Ring Description for Cyclic Convolutional Codes

2007-08-09

arxiv.org/abs/0708.1343v1

Computer Science

Information Theory

Scientific paper

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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