A New Perspective of Cyclicity in Convolutional Codes


In this paper, we propose a new way of providing cyclic structures to convolutional codes. We have a tendency to define the skew cyclic convolutional codes as left ideals of a quotient ring of a suitable non-commutative polynomial ring. In distinction to the previous approaches to cyclicity for convolutional codes, we tend to use Ore polynomials with coefficients in a very field (the rational perform field over a finite field), therefore their arithmetic is terribly well-known and we have a tendency to could proceed similarly to cyclic block codes. In specific, we show how to obtain simply skew cyclic convolutional codes of a given dimension, and we have a tendency to compute an idempotent generator of the code and its dual.

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