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Title: Basic Algorithms for Manipulation of Modules over Finite Chain Rings
Authors: Georgieva, Nevyana
Keywords: Chain Rings
Finitely Generated Modules over Finite Chain Rings
The Orthogonal Module
Linear Codes over Finite Chain Rings
Standard Form of a Matrix over a Chain Ring
Issue Date: 2016
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Journal of Computing, Vol. 10, No 3-4, (2016), 285p-297p
Abstract: In this paper, we present some basic algorithms for manipulation of finitely generated modules over finite chain rings. We start with an algorithm that generates the standard form of a matrix over a finite chain ring, which is an analogue of the row reduced echelon form for a matrix over a field. Furthermore we give an algorithm for the generation of the union of two modules, an algorithm for the generation of the orthogonal module to a given module, as well as an algorithm for the generation of the intersection of two modules. Finally, we demonstrate how to generate all submodules of fixed shape of a given module. ACM Computing Classification System (1998): G.1.3, G.4.
ISSN: 1312-6555
Appears in Collections:Volume 10 Number 3-4

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