Abstract
In this work we focus on a connection between sumsets and covering codes in an arbitrary finite module. For this purpose, bounds on a new problem on sumsets are obtained from well-known results of additive number theory, namely, the Cauchy-Davenport theorem, the Vosper theorem and a theorem due to Hamidoune-Rodseth. As an application, the approach is able to extend the Blokhuis-Lam theorems and a construction of covering codes by Honkala to an arbitrary module.
Highlights
Let X be a commutative ring with identity and cardinality q ≥ 2
As a goal of this work, we extend the constructions by Blokhuis-Lam [1] and Honkala
We conclude this work with a connection between sum sets, covering codes, and short coverings in Section 6, extending a result due to
Summary
Xn can be regarded as a module over X. The so-called matrix method is a powerful tool even for nonlinear covering code. [17] generalized the matrix method to an arbitrary radius R. As a goal of this work, we extend the constructions by Blokhuis-Lam [1] and Honkala [10] to an arbitrary finite module. The function Pk (X, A) allows us to review and extend some known constructions of covering codes by using the matrix method. As another goal, we conclude this work with a connection between sum sets, covering codes, and short coverings, extending a result due to Blokhuis-Lam We conclude this work with a connection between sum sets, covering codes, and short coverings in Section 6, extending a result due to Blokhuis-Lam
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