Some results on cyclic codes over \(\mathbb{Z}_q + u\mathbb{Z}_q\) (Q2788736)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Some results on cyclic codes over \(\mathbb{Z}_q + u\mathbb{Z}_q\) |
scientific article; zbMATH DE number 6543453
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some results on cyclic codes over \(\mathbb{Z}_q + u\mathbb{Z}_q\) |
scientific article; zbMATH DE number 6543453 |
Statements
22 February 2016
0 references
cyclic codes
0 references
minimum generating sets
0 references
free cyclic codes
0 references
BCH bound
0 references
Some results on cyclic codes over \(\mathbb{Z}_q + u\mathbb{Z}_q\) (English)
0 references
Let \(R=\mathbb Z_q+u\mathbb Z_q\), where \(q=p^s\) for some prime \(p\) and \(u^2=0\). Authors have obtained the minimum generating sets of cyclic codes over \(R\). A necessary and sufficient condition for cyclic codes over \(R\) to be \(R\)-free is obtained. Further it is shown that the minimum Hamming distance of a cyclic code over \(R\) satisfies a BCH-type bound like a cyclic code over a finite field.
0 references
