2 research outputs found
Codes over Affine Algebras with a Finite Commutative Chain coefficient Ring
We consider codes defined over an affine algebra , where
is a monic univariate polynomial over a finite commutative chain
ring . Namely, we study the submodules of (). These codes generalize both the codes over finite quotients of
polynomial rings and the multivariable codes over finite chain rings. {Some
codes over Frobenius local rings that are not chain rings are also of this
type}. A canonical generator matrix for these codes is introduced with the help
of the Canonical Generating System. Duality of the codes is also considered.Comment: Submitted to Finite Fields and Their Application
Quasi-Cyclic Codes Over Finite Chain Rings
In this paper, we mainly consider quasi-cyclic (QC) codes over finite chain
rings. We study module structures and trace representations of QC codes, which
lead to some lower bounds on the minimum Hamming distance of QC codes.
Moreover, we investigate the structural properties of 1-generator QC codes.
Under some conditions, we discuss the enumeration of 1-generator QC codes and
describe how to obtain the one and only one generator for each 1-generator QC
code.Comment: 2