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- Publisher Website: 10.3934/amc.2008.2.55
- Scopus: eid_2-s2.0-70349310363
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Article: A matrix ring description for cyclic convolutional codes
| Title | A matrix ring description for cyclic convolutional codes |
|---|---|
| Authors | |
| Keywords | Convolutional codes Cyclic codes Forney indices Skew polynomial rings |
| Issue Date | 1-Feb-2008 |
| Publisher | American Institute of Mathematical Sciences (AIMS) |
| Citation | Advances in Mathematics of Communications, 2008, v. 2, n. 1, p. 55-81 How to Cite? |
| Abstract | In this paper, we study convolutional codes with a specific cyclic structure. By definition, these codes are left ideals in a certain skew polynomial ring. Using that the skew polynomial ring is isomorphic to a matrix ring we can describe the algebraic parameters of the codes in a more accessible way. We show that the existence of such codes with given algebraic parameters can be reduced to the solvability of a modified rook problem. It is our strong belief that the rook problem is always solvable, and we present solutions in particular cases. |
| Persistent Identifier | http://hdl.handle.net/10722/357122 |
| ISSN | 2023 Impact Factor: 0.7 2023 SCImago Journal Rankings: 0.463 |
| ISI Accession Number ID |
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | Gluesing-Luerssen, Heide | - |
| dc.contributor.author | Tsang, Fai-Lung | - |
| dc.date.accessioned | 2025-06-23T08:53:29Z | - |
| dc.date.available | 2025-06-23T08:53:29Z | - |
| dc.date.issued | 2008-02-01 | - |
| dc.identifier.citation | Advances in Mathematics of Communications, 2008, v. 2, n. 1, p. 55-81 | - |
| dc.identifier.issn | 1930-5346 | - |
| dc.identifier.uri | http://hdl.handle.net/10722/357122 | - |
| dc.description.abstract | <p>In this paper, we study convolutional codes with a specific cyclic structure. By definition, these codes are left ideals in a certain skew polynomial ring. Using that the skew polynomial ring is isomorphic to a matrix ring we can describe the algebraic parameters of the codes in a more accessible way. We show that the existence of such codes with given algebraic parameters can be reduced to the solvability of a modified rook problem. It is our strong belief that the rook problem is always solvable, and we present solutions in particular cases.<br></p> | - |
| dc.language | eng | - |
| dc.publisher | American Institute of Mathematical Sciences (AIMS) | - |
| dc.relation.ispartof | Advances in Mathematics of Communications | - |
| dc.rights | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | - |
| dc.subject | Convolutional codes | - |
| dc.subject | Cyclic codes | - |
| dc.subject | Forney indices | - |
| dc.subject | Skew polynomial rings | - |
| dc.title | A matrix ring description for cyclic convolutional codes | - |
| dc.type | Article | - |
| dc.identifier.doi | 10.3934/amc.2008.2.55 | - |
| dc.identifier.scopus | eid_2-s2.0-70349310363 | - |
| dc.identifier.volume | 2 | - |
| dc.identifier.issue | 1 | - |
| dc.identifier.spage | 55 | - |
| dc.identifier.epage | 81 | - |
| dc.identifier.eissn | 1930-5338 | - |
| dc.identifier.isi | WOS:000254707800004 | - |
| dc.identifier.issnl | 1930-5338 | - |