Primitive idempotents in central simple algebras over 𝔽_q(t) with an application to coding theory

06/22/2020

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by   J. Gómez-Torrecillas, et al.

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We consider the algorithmic problem of computing a primitive idempotent of a central simple algebra over the field of rational functions over a finite field. The algebra is given by a set of structure constants. The problem is reduced to the computation of a division algebra Brauer equivalent to the central simple algebra. This division algebra is constructed as a cyclic algebra, once the Hasse invariants have been computed. We give an application to skew constacyclic convolutional codes.