Some results on the structure of constacyclic codes and new linear codes over 
GF(7) from quasi-twisted codes

Aydin, Nuh; Connolly, Nicholas; Grassl, Markus

doi:10.3934/amc.2017016

Item

ITEM ACTIONSEXPORT

Add to Basket

Local TagsRelease HistoryDetailsSummary

Released

Journal Article

Some results on the structure of constacyclic codes and new linear codes over GF(7) from quasi-twisted codes

MPS-Authors

/persons/resource/persons201075

Grassl, Markus
Quantumness, Tomography, Entanglement, and Codes, Leuchs Division, Max Planck Institute for the Science of Light, Max Planck Society;

External Resource

No external resources are shared

Fulltext (restricted access)

There are currently no full texts shared for your IP range.

Fulltext (public)

There are no public fulltexts stored in PuRe

Supplementary Material (public)

There is no public supplementary material available

Citation

Aydin, N., Connolly, N., & Grassl, M. (2017). Some results on the structure of constacyclic codes and new linear codes over GF(7) from quasi-twisted codes. ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 11(1), 245-258. doi:10.3934/amc.2017016.

Cite as: https://hdl.handle.net/21.11116/0000-0000-7DEB-C

Abstract

One of the most important and challenging problems in coding theory is to construct codes with good parameters. There are various methods to construct codes with the best possible parameters. A promising and fruitful approach has been to focus on the class of quasi-twisted (QT) codes which includes constacyclic codes as a special case. This class of codes is known to contain many codes with good parameters. Although constacyclic codes and QT codes have been the subject of numerous studies and computer searches over the last few decades, we have been able to discover a new fundamental result about the structure of constacyclic codes which was instrumental in our comprehensive search method for new QT codes over GF(7). We have been able to find 41 QT codes with better parameters than the previously best known linear codes. Furthermore, we derived a number of additional new codes via Construction X as well as standard constructions, such as shortening and puncturing.