A Matrix Ring Description for Cyclic Convolutional Codes

: 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.

• Type: Journal
• Year: 2007
• Where: CORR
• Authors: Heide Gluesing-Luerssen, Fai-Lung Tsang
• Keywords: Certain Skew Polynomial, CORR 2007, Education, Skew Polynomial, Skew Polynomial Ring