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.

中文翻译：

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Fq(t) 上的中心简单代数中的原始幂等性以及在编码理论中的应用

我们考虑在有限域上的有理函数域上计算中心简单代数的原始幂等的算法问题。代数由一组结构常数给出。问题被简化为等价于中心简单代数的除法代数 Brauer 的计算。一旦计算了 Hasse 不变量，这个除法代数就被构造为循环代数。我们给出了一个歪斜恒循环卷积码的应用。