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

2020/06/22 by José Gómez-Torrecillas, Gómez-Torrecillas, J., Péter Kutas +5 · 1 citation
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Computer and information sciences #FOS: Mathematics #Finite Group Theory Research #Information Theory (cs.IT) #Number Theory (math.NT) #Rings and Algebras (math.RA) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2006.12116

openalex publication_date 2020/06/22 · openalex created_date 2020/06/25 · openalex updated_date 2026/07/28

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.

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