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
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Journal of Computing, Vol. 10, No 3-4, (2016), 285p-297p
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.