A new perspective of cyclicity in convolutional codes
J Gómez-Torrecillas, FJ Lobillo… - IEEE Transactions on …, 2016 - ieeexplore.ieee.org
IEEE Transactions on Information Theory, 2016•ieeexplore.ieee.org
In this paper, we propose a new way of providing cyclic structures to convolutional codes.
We define the skew cyclic convolutional codes as left ideals of a quotient ring of a suitable
non-commutative polynomial ring. In contrast to the previous approaches to cyclicity for
convolutional codes, we use Ore polynomials with coefficients in a field (the rational function
field over a finite field), so their arithmetic is very well known and we may proceed similarly
to cyclic block codes. In particular, we show how to obtain easily skew cyclic convolutional …
We define the skew cyclic convolutional codes as left ideals of a quotient ring of a suitable
non-commutative polynomial ring. In contrast to the previous approaches to cyclicity for
convolutional codes, we use Ore polynomials with coefficients in a field (the rational function
field over a finite field), so their arithmetic is very well known and we may proceed similarly
to cyclic block codes. In particular, we show how to obtain easily skew cyclic convolutional …
In this paper, we propose a new way of providing cyclic structures to convolutional codes. We define the skew cyclic convolutional codes as left ideals of a quotient ring of a suitable non-commutative polynomial ring. In contrast to the previous approaches to cyclicity for convolutional codes, we use Ore polynomials with coefficients in a field (the rational function field over a finite field), so their arithmetic is very well known and we may proceed similarly to cyclic block codes. In particular, we show how to obtain easily skew cyclic convolutional codes of a given dimension, and we compute an idempotent generator of the code and its dual.
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