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Primitive idempotents in central simple algebras over Fq(t) with an application to coding theory |
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| Institution: | 1. IMAG and Department of Algebra, University of Granada, E18071, Granada, Spain;2. School of Computer Science, University of Birmingham, B15 2TT, Birmingham, United Kingdom;3. CITIC and Department of Algebra, University of Granada, E18071, Granada, Spain;4. CITIC and Department of Computer Science and A. I., University of Granada, E18071, Granada, Spain |
| Abstract: | 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. |
| Keywords: | Global function field Central simple algebra Hasse invariants Primitive idempotent Skew constacyclic convolutional code |
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