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

被引：2

作者：

Gomez-Torrecillas, J. ^{[1
,2
]}

Kutas, P. ^{[3
]}

Lobillo, F. J. ^{[2
,4
]}

Navarro, G. ^{[4
,5
]}

机构：

[1] Univ Granada, IMAG, E-18071 Granada, Spain

[2] Univ Granada, Dept Algebra, E-18071 Granada, Spain

[3] Univ Birmingham, Sch Comp Sci, Birmingham B15 2TT, W Midlands, England

[4] Univ Granada, CITIC, E-18071 Granada, Spain

[5] Univ Granada, Dept Comp Sci & AI, E-18071 Granada, Spain

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2022年 / 77卷

关键词：

Global function field; Central simple algebra; Hasse invariants; Primitive idempotent; Skew constacyclic convolutional code; FULL MATRIX ALGEBRAS; ALGORITHM;

D O I：

10.1016/j.ffa.2021.101935

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (c) 2021 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

引用

页数：18

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